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Paper Citation Record · LEDGER

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems

As of 17 August 2026, this Paper Citation Record lists 78 of 78 outbound references and 1 inbound Pith citation observation for arXiv:2412.03970.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2412.03970 v2

Coverage vector

measured 78 of 78 reference resolution

Typed states for the displayed outbound observations.

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measured 79 of 79 standing notices

One-hop event checks from named stored sources.

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measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-30T13:41:08.413795Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

78 of 78 outbound references displayed

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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 6ac35b80-18c0-4614-ab0b-ea9ae67848e9 · outbound

This paper cites Deep learning and process understanding for data-driven earth system science.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Deep learning and process understanding for data-driven earth system science

Reference 1

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Observation ea676e1a-1694-478a-bde5-91da6f135add · outbound

This paper cites Data-driven methods for flow and transport in porous media: A review.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Data-driven methods for flow and transport in porous media: A review

Reference 2

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Observation 6bf4b8cc-79d0-405c-b243-0d28fa6c689b · outbound

This paper cites Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations

Reference 3

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Observation b1da8b35-4c91-45ed-aeb1-e39d84286131 · outbound

This paper cites Promising directions of machine learning for partial di fferential equations.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Promising directions of machine learning for partial di fferential equations

Reference 4

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Observation a1d133a4-abb8-48a8-acd1-d94517012f1e · outbound

This paper cites Uncovering terrain-precipitation equation with inter- pretable AI: Towards future climate projection.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Uncovering terrain-precipitation equation with inter- pretable AI: Towards future climate projection

Reference 5

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Observation d15ea15d-60fa-40b1-8d41-cf4233f84797 · outbound

This paper cites Genetic programming as a means for programming computers by natural selection.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Genetic programming as a means for programming computers by natural selection

Reference 6

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Observation b13ac82b-e7a6-4398-afc5-d3c7eb8b0490 · outbound

This paper cites Automated reverse engineering of nonlinear dynamical systems.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Automated reverse engineering of nonlinear dynamical systems

Reference 7

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Observation 033a1301-ffa8-4f7f-9e31-3a7e36a0cf44 · outbound

This paper cites Distilling free-form natural laws from experimental data.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Distilling free-form natural laws from experimental data

Reference 8

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Observation c185be6b-058f-4bb4-aced-7e2f22eacf4b · outbound

This paper cites Discovering governing equations from data by sparse identification of nonlinear dynamical systems.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Discovering governing equations from data by sparse identification of nonlinear dynamical systems

Reference 9

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Observation 230d5cf3-9881-4b89-b561-5f3c253ec4fa · outbound

This paper cites Data-driven discovery of partial di fferential equations.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Data-driven discovery of partial di fferential equations

Reference 10

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Observation a908e4af-c8d7-4044-a323-c115df1aa85b · outbound

This paper cites Machine learning subsurface flow equations from data.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Machine learning subsurface flow equations from data

Reference 11

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Observation b8e0308e-48a1-44d0-a3f9-52bdcd48c27e · outbound

This paper cites Weak SINDy for partial di fferential equations.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Weak SINDy for partial di fferential equations

Reference 12

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Observation 858e1d3e-04dc-494c-9ac8-14834fa002f7 · outbound

This paper cites Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control

Reference 13

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Observation 786b13ae-0878-4159-858f-48e1d8fbb014 · outbound

This paper cites Robust data-driven dynamic model discovery of industrial robots with spatial manipulation capability using simple trajectory.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Robust data-driven dynamic model discovery of industrial robots with spatial manipulation capability using simple trajectory

Reference 14

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Observation 880d22dd-d7a9-4ef1-8fac-3c212cb87b3a · outbound

This paper cites Discovering governing equation from data for multi-stable energy harvester under white noise.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Discovering governing equation from data for multi-stable energy harvester under white noise

Reference 15

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Observation ed368419-6491-4c47-883d-0460e5179da2 · outbound

This paper cites DL-PDE: Deep-learning based data-driven discovery of partial differential equations from discrete and noisy data.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems DL-PDE: Deep-learning based data-driven discovery of partial differential equations from discrete and noisy data

Reference 16

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Observation 77117b0b-ea71-4441-9090-34aed5b3ed81 · outbound

This paper cites DeepMoD: Deep learning for model discovery in noisy data.Journal of Computational Physics, 428:109985, 2021.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems DeepMoD: Deep learning for model discovery in noisy data.Journal of Computational Physics, 428:109985, 2021

Reference 17

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Observation 51e3d9cd-4d01-4527-9afc-c6591e6c0bd0 · outbound

This paper cites Integration of knowledge and data in machine learning.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Integration of knowledge and data in machine learning

Reference 18

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Observation d74348cf-9e57-4500-98b5-ba6af3db29ee · outbound

This paper cites Robust discovery of partial di fferential equations in complex situations.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Robust discovery of partial di fferential equations in complex situations

Reference 19

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Observation 04f4f5a3-03d4-4b29-9f3a-ac4a9854192a · outbound

This paper cites Metzler and J.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Metzler and J

Reference 20

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Observation 3c4ba516-9447-4f32-bfe6-26915d03761d · outbound

This paper cites Mechanisms, upscaling, and prediction of anomalous dispersion in heterogeneous porous media.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Mechanisms, upscaling, and prediction of anomalous dispersion in heterogeneous porous media

Reference 21

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Observation 5796f787-fa24-4f70-9dd1-5ec04457f2bc · outbound

This paper cites Data-driven identification of parametric partial di fferential equa- tions.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Data-driven identification of parametric partial di fferential equa- tions

Reference 22

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Observation d3c28e04-c68b-4356-98e9-c0314849c19b · outbound

This paper cites Wheatcraft and Scott W Tyler.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Wheatcraft and Scott W Tyler

Reference 23

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Observation 013b3bf7-82cc-438b-9e5c-7d374bbfe4ab · outbound

This paper cites A review and numerical assessment of the random walk particle tracking method.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems A review and numerical assessment of the random walk particle tracking method

Reference 24

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Observation 35280e3a-daab-4002-a2a2-ca6baa8142a7 · outbound

This paper cites Deep-learning based discovery of partial differential equations in integral form from sparse and noisy data.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Deep-learning based discovery of partial differential equations in integral form from sparse and noisy data

Reference 25

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Observation 95abf519-234c-4d3f-9598-d834a0db5d86 · outbound

This paper cites Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE).

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE)

Reference 26

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Observation 46d831a9-d918-4444-af09-67b3d3ba1a66 · outbound

This paper cites The data-driven discovery of partial di fferential equations by symbolic genetic algorithm.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems The data-driven discovery of partial di fferential equations by symbolic genetic algorithm

Reference 27

Resolution
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Observation 0c6b5653-256a-45d8-aa1f-8d3350e361d7 · outbound

This paper cites DISCOVER: Deep identification of symbolically concise open-form partial differential equations via enhanced reinforcement learning.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems DISCOVER: Deep identification of symbolically concise open-form partial differential equations via enhanced reinforcement learning

Reference 28

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Observation dc40b6d2-c258-4cae-afc1-353d85e68d8b · outbound

This paper cites Physics-constrained robust learning of open-form partial differential equations from limited and noisy data.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Physics-constrained robust learning of open-form partial differential equations from limited and noisy data

Reference 29

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Observation 116030ef-db66-46a0-bc2b-2300b272e331 · outbound

This paper cites LLM4ED: Large Language Models for Automatic Equation Discovery.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems LLM4ED: Large Language Models for Automatic Equation Discovery

Reference 30

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Observation 0e82f51e-c4ce-4954-aba7-374c6ccfae79 · outbound

This paper cites Physics-informed deep neural networks for learning parameters and constitutive relationships in subsurface flow problems.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Physics-informed deep neural networks for learning parameters and constitutive relationships in subsurface flow problems

Reference 31

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Observation bc7b71ea-cc4b-40c2-a8d3-c2986c22f26a · outbound

This paper cites Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the glue methodology.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the glue methodology

Reference 32

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Observation 670ef3d8-5a6d-420c-87ae-fd15c2d4efc4 · outbound

This paper cites Field study of dispersion in a heterogeneous aquifer: 2.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Field study of dispersion in a heterogeneous aquifer: 2

Reference 33

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Observation 6c64d6f2-759e-403d-8d82-e5aade978287 · outbound

This paper cites Cushman, Lynn S.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Cushman, Lynn S

Reference 34

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 463ea71f-712e-4cdd-9aef-e391fce842b7 · outbound

This paper cites an unresolved cited work.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Unresolved cited work

Reference 35

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unresolved
raw_fallback, observed 2026-08-11T21:58:12.767294Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 99ef00aa-860e-432c-8c6d-1fdf0a1fba88 · outbound

This paper cites Theory of solute transport by groundwater.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Theory of solute transport by groundwater

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.756717Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.051781Z digest=sha256:5c878dde905e9531fa0361d3fd07d154e9382c087685731059c3dd1c806f7000

Observation 86a3bfeb-4f45-4050-8c50-dea86f018ea7 · outbound

This paper cites Modeling non-fickian transport in geological formations as a continuous time random walk.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Modeling non-fickian transport in geological formations as a continuous time random walk

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.746889Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.055503Z digest=sha256:f12cf4a021ae4aa3f0b4d2340829e3b3b2ccef437b5dd7f42c5e503ec2186f1e

Observation 3a2ec802-8365-4c11-abb0-ca4f73f1c34c · outbound

This paper cites Application of a fractional advection-dispersion equation.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Application of a fractional advection-dispersion equation

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.736648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 9a794423-67fe-46db-8d80-c6022a22a4ca · outbound

This paper cites Multiple-rate mass transfer for modeling di ffusion and surface reactions in media with pore-scale heterogeneity.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Multiple-rate mass transfer for modeling di ffusion and surface reactions in media with pore-scale heterogeneity

Reference 39

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.062993Z digest=sha256:27cc8c9398c2843c7f04efa976be4787b7cb826e5bba9addb197ba25e29ce81a

Observation 1870158c-8215-4bdd-96a3-9e6edd26a9cd · outbound

This paper cites Theory and applications of fractional di fferential equations, volume 204.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Theory and applications of fractional di fferential equations, volume 204

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.714348Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.066571Z digest=sha256:e58494672409c2652340434a9775d9539c2590ae1bed5bfaca0413e1a5e34373

Observation 8283151e-e9c3-4299-a2b6-18b669b1f278 · outbound

This paper cites Podlubny.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Podlubny

Reference 41

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.702876Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.070412Z digest=sha256:583f2a7b59b2c828836eb81c22e6c2d5ad647e5e28dc224defadd7c21539c95f

Observation a5bd4bd1-0edc-448c-99cd-c90b094d7648 · outbound

This paper cites Stochastic models for fractional calculus , volume 43.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Stochastic models for fractional calculus , volume 43

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.692283Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.074357Z digest=sha256:398d519bc4ea4b6ff8b47051eee502c70d63d2aed13d3708cdc981a7cef607cc

Observation 5aec98eb-8f92-4267-9858-e137e7263122 · outbound

This paper cites Fractional partial differential equations and their numerical solutions.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Fractional partial differential equations and their numerical solutions

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.681117Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.078449Z digest=sha256:0a7f7728bec30b615cc8489f772f352a4315c5e541239448b2d16b4f78df5164

Observation 24b4d95e-8069-41fe-9279-181cc4df9812 · outbound

This paper cites A new collection of real world applications of fractional calculus in science and engineering.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems A new collection of real world applications of fractional calculus in science and engineering

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.668216Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.082597Z digest=sha256:b39b139290789b12d486333543852260691d8f2204f3cfc7c7981025323242ff

Observation 624a8e39-ee5f-461f-a2ff-9338698f4468 · outbound

This paper cites A space fractional constitutive equation model for non-newtonian fluid flow.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems A space fractional constitutive equation model for non-newtonian fluid flow

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.656747Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.086275Z digest=sha256:0327984a837d50a5e210c1b5847788db50100ddcb2db97a2bee5db2826aa44fc

Observation 93b7a8bc-b5c2-4bf0-8a83-3ca18ac2b9cf · outbound

This paper cites Generalized viscoelastic models: their fractional equations with solutions.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Generalized viscoelastic models: their fractional equations with solutions

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.645752Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.089888Z digest=sha256:089d12493cb61b8c45f0dfcaf0bc0dfb7404dd064f31afc710f582ad8958b426

Observation a694ea62-b080-4acc-86be-462376b662ac · outbound

This paper cites Fractional calculus and continuous-time finance.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Fractional calculus and continuous-time finance

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.634888Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.093554Z digest=sha256:3367f264734b442a853cd8cffdb9f03d229c6eeb9844788c0513de659bd49bbd

Observation 20ab25c6-9f62-4b43-870e-ed14b6d1f1a0 · outbound

This paper cites Using gauss-jacobi quadrature rule to improve the accuracy of fem for spatial fractional problems.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Using gauss-jacobi quadrature rule to improve the accuracy of fem for spatial fractional problems

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.623874Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.097134Z digest=sha256:9dc0088297d4c603b56ad646380c5d94f656fbdc83d65eef393f74920fe8d4d7

Observation a5f2659a-bb2e-447f-9891-57956695d568 · outbound

This paper cites fpinns: Fractional physics-informed neural networks.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems fpinns: Fractional physics-informed neural networks

Reference 49

Resolution
unresolved
no resolver link, observed 2026-08-11T21:58:12.100610Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T21:58:12.100610Z digest=sha256:debdc944b669b1d6be852cd78ff812ff90d58bf47adfb5a97f39983b61ba5dea

Observation bb1cb30d-6d78-4549-b7ba-cb9fc5dca64c · outbound

This paper cites Machine learning of space-fractional di fferential equations.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Machine learning of space-fractional di fferential equations

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.607156Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.105053Z digest=sha256:76abffa1b89daec27ca6abedf714f50a88fd9824f596a8d59cf6adb7ca49a92a

Observation aeff6f15-2c0c-456b-8d97-2bd25aad11f4 · outbound

This paper cites Coelho, M.Fernanda P.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Coelho, M.Fernanda P

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.596601Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.108804Z digest=sha256:2653159889dad02ad08a15fda1b9df93a536a6d67f38eca5b71acb4a40c66cb6

Observation 97d29150-9e87-4724-a1fc-ad7d1ee725ae · outbound

This paper cites Neural fractional di fferential equations.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Neural fractional di fferential equations

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.586060Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

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Observation 587096d1-4346-4dc3-b654-8da883c9afce · outbound

This paper cites Data-driven discovery of time fractional di fferential equations.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Data-driven discovery of time fractional di fferential equations

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.575665Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.116157Z digest=sha256:8269b69968e9363512ecf25de71f6defbfb17dcfe6780f1b2a0f408d3a4391c7

Observation e57db67c-2fa2-492e-a036-8c8986148289 · outbound

This paper cites A new perspective for scientific modelling: Sparse reconstruction- based approach for learning time-space fractional di fferential equations.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems A new perspective for scientific modelling: Sparse reconstruction- based approach for learning time-space fractional di fferential equations

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.565491Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.119934Z digest=sha256:7a089b0d2084d1a6ad5d20e3889dc2643037d662990f24cbd179af6e598bbe54

Observation 649da173-b66e-4dba-bd2e-f9a3389c2c63 · outbound

This paper cites Gauss-Jacobi-type quadrature rules for fractional directional integrals.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Gauss-Jacobi-type quadrature rules for fractional directional integrals

Reference 55

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.554881Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.123604Z digest=sha256:eadabb494003c904b14a168fb78cd35683ea86d86d877d3dc7567b830a2308ee

Observation 5928539a-984e-4a80-8a3d-9170d68f5ad0 · outbound

This paper cites Physics-informed learning of governing equations from scarce data.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Physics-informed learning of governing equations from scarce data

Reference 56

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.544633Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.127070Z digest=sha256:ac65c72c4bbae166e162b7864370cbc25f28fcab934137520bf7ec48d294f539

Observation 5954f211-4e62-415e-af82-bcaeb702887a · outbound

This paper cites Discovery of subdi ffusion problem with noisy data via deep learning.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Discovery of subdi ffusion problem with noisy data via deep learning

Reference 57

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.533200Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.130780Z digest=sha256:67d7899f0a1a3d4ee5449b8b1f1caffcbc051f4340e58767cc1a2b56d3ae51ac

Observation 12c2c564-6502-4da6-a6f5-4f1521008dbe · outbound

This paper cites Deep hidden physics models: Deep learning of nonlinear partial di fferential equations.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Deep hidden physics models: Deep learning of nonlinear partial di fferential equations

Reference 58

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.523249Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.134399Z digest=sha256:aa69b16320fbbf0f896f27f445723b685293eea3a4945fd740c9ffd28afc1d4c

Observation 07950fce-a5b3-4123-92e2-99e3298b3a09 · outbound

This paper cites Particle swarm fractional order derivative model of artificial frozen soil creep properties.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Particle swarm fractional order derivative model of artificial frozen soil creep properties

Reference 59

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.512637Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.138032Z digest=sha256:5ad7cb97853e9e1c2adecd9a2a5fb6148372a3fde5f0a3568fa6009e9e5a8a1c

Observation e6425978-7d01-44f3-a804-55f35a15c759 · outbound

This paper cites Time and space nonlocalities underlying fractional-derivative models: Distinction and literature review of field applications.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Time and space nonlocalities underlying fractional-derivative models: Distinction and literature review of field applications

Reference 60

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.501900Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.141967Z digest=sha256:3610c90f330e7a53dfbfbbf20c49330353d2453119c61e4f8bd2afb32e166d84

Observation f3cf89fd-eb96-4b24-ad7d-b455e725de00 · outbound

This paper cites Data-driven discovery of governing equations for fluid dynamics based on molecular simulation.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Data-driven discovery of governing equations for fluid dynamics based on molecular simulation

Reference 61

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.491366Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.145441Z digest=sha256:0dc1a61408f37e973bf3abb167f1b8266237f093d4bca5bdafeb01ae48a40596

Observation 015452fb-1faa-4f46-8ecc-803abe187306 · outbound

This paper cites Limit distributions for sums of independent random variables, volume 233.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Limit distributions for sums of independent random variables, volume 233

Reference 62

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.480210Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.148739Z digest=sha256:14becbb2e1929725bae7d7a5bb150eae24e46594b2892310e9fedfd8830a1bed

Observation a06509d7-e3aa-4513-88f2-cf5afd8971cf · outbound

This paper cites Fractional dispersion, Lévy motion, and the made tracer tests.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Fractional dispersion, Lévy motion, and the made tracer tests

Reference 63

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.468418Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.154617Z digest=sha256:e4f249d47112f637443c62864daa60cd0744af8f0f4a5961fc2e7c70d825a675

Observation 5d6e75f4-ac2a-4492-842e-5a364a925d91 · outbound

This paper cites Théorie de l’addition des variables aléatoires.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Théorie de l’addition des variables aléatoires

Reference 64

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.456076Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.158486Z digest=sha256:540f8b3e851b3f79b118cf297a04112f0a75fbf690c958d63932dbe73ed1896f

Observation 55608b7c-ca4b-47da-aab4-f151d11a380b · outbound

This paper cites DLGA-PDE: Discovery of pdes with incomplete candidate library via combination of deep learning and genetic algorithm.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems DLGA-PDE: Discovery of pdes with incomplete candidate library via combination of deep learning and genetic algorithm

Reference 65

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.444090Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.162201Z digest=sha256:f09c043f06ac039596757d501539c07ff89cc983adf43cf1a8eda2458233c72d

Observation ac1111f5-96d2-4db6-a375-d15f82b2c542 · outbound

This paper cites Neural fractional di fferential equations: Optimising the order of the fractional 19 derivative.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Neural fractional di fferential equations: Optimising the order of the fractional 19 derivative

Reference 66

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.431430Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.165705Z digest=sha256:eaa115bfa779334b31c619221af7a0371bd08f49ebf5e1c349ea52b2c3da5fc2

Observation 07135f55-a528-4a42-938d-230da5dd8c51 · outbound

This paper cites Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FROND.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Unleashing the Potential of Fractional Calculus in Graph Neural Networks with FROND

Reference 67

Resolution
unresolved
no resolver link, observed 2026-08-11T21:58:12.169386Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T21:58:12.169386Z digest=sha256:2ca6b4d8a0ce276515973bf5e124058e520bf322201731556a2f9e9bf2b26b6a

Observation d7166941-0c1c-4705-8b64-e4e44d87e549 · outbound

This paper cites Fde-net: A memory-e fficiency densely connected network inspired from fractional-order differential equations for single image super-resolution.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Fde-net: A memory-e fficiency densely connected network inspired from fractional-order differential equations for single image super-resolution

Reference 68

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.419400Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

source=pdf_text observed=2026-08-11T21:58:12.173444Z digest=sha256:56f431730d2bb18a0e5633bb505a8419ce7baea6cc5212624dceb954f402befb

Observation e5ee93ae-bb99-49af-befb-e1ad7160f2f7 · outbound

This paper cites Optimising neural fractional di fferential equations for performance and efficiency.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Optimising neural fractional di fferential equations for performance and efficiency

Reference 69

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T21:58:12.406353Z

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This paper cites Neural variable-order fractional differential equation networks.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Neural variable-order fractional differential equation networks

Reference 70

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This paper cites Efficient training of neural fractional-order differential equation via adjoint backpropagation.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Efficient training of neural fractional-order differential equation via adjoint backpropagation

Reference 71

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Observation b782da2b-dc64-4e80-92ab-b05cd45b0554 · outbound

This paper cites Spectral methods: algorithms, analysis and applications, volume 41.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Spectral methods: algorithms, analysis and applications, volume 41

Reference 72

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Observation 13d8e715-2932-4785-8902-4a8c73be669c · outbound

This paper cites Theory and Numerical Approximations of Fractional Integrals and Derivatives.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Theory and Numerical Approximations of Fractional Integrals and Derivatives

Reference 73

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This paper cites Calculation of gauss quadrature rules.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Calculation of gauss quadrature rules

Reference 74

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Observation e0e573d1-b8b2-486d-8d68-617212393c5f · outbound

This paper cites Lin and C.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Lin and C

Reference 75

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Observation 03e64fb9-4857-40a7-8091-3f9a3161e7b9 · outbound

This paper cites An introduction to probability theory and its applications, Volume 2 , volume 81.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems An introduction to probability theory and its applications, Volume 2 , volume 81

Reference 76

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This paper cites On using random walks to solve the space-fractional advection-dispersion equations.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems On using random walks to solve the space-fractional advection-dispersion equations

Reference 77

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This paper cites Parameterizations and modes of stable distributions.

A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems Parameterizations and modes of stable distributions

Reference 78

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On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement cites this paper.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement A Data-Driven Framework for Discovering Fractional Differential Equations in Complex Systems

Reference 112

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