For regular Volterra kernels the square-root process obeys a time-dependent Feller condition and stays positive; for rough regularly-varying kernels it hits zero with positive probability and carries an atom at the boundary.
Luchko,General fractional integrals and derivatives with the Sonine kernels, Mathematics9(2021), 594
2 Pith papers cite this work. Polarity classification is still indexing.
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Proves well-posedness of weighted fractional operators via deformed translation semigroups using amnesia weights, bypassing Bernstein function restrictions.
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Boundary behaviour of the Volterra square-root process
For regular Volterra kernels the square-root process obeys a time-dependent Feller condition and stays positive; for rough regularly-varying kernels it hits zero with positive probability and carries an atom at the boundary.
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A Semigroup Approach to Weighted Weyl-Sonine Operators: Bypassing Bernstein Functions for Well-Posedness
Proves well-posedness of weighted fractional operators via deformed translation semigroups using amnesia weights, bypassing Bernstein function restrictions.