{"paper":{"title":"On Space-Time Fractional Heat Type Non-Homogeneous Time-Fractional Poisson Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ejighikeme McSylvester Omaba","submitted_at":"2017-06-11T19:28:57Z","abstract_excerpt":"Consider the following space-time fractional heat equation with Riemann-Liouville derivative of non-homogeneous time-fractional Poisson process \\begin{eqnarray*} \\partial^\\beta_t u(x,t) =-\\kappa(-\\Delta)^{\\alpha/2} u(x,t) + I_t^{1-\\beta}[\\sigma(u)D_t^\\vartheta N^\\nu_\\lambda(t)], \\,\\, t\\geq 0, \\,x \\in \\mathbb{R}^d, \\end{eqnarray*} where $\\kappa>0, \\,\\,\\beta,\\,\\vartheta\\in(0,1), \\,\\,\\nu\\in(0,1],\\,\\alpha\\in(0,2].$ The operator $D_t^\\vartheta N^\\nu_\\lambda(t) = \\frac{\\rm d}{\\mathrm{d} t} I_t^{1-\\vartheta} N_\\lambda^\\nu(t) = \\frac{\\rm d}{\\mathrm{d} t} \\mathcal{N}_\\lambda^{1-\\vartheta,\\nu}(t)$ with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.03394","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}