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A Numerical Scheme for a Generalized Fractional Derivative with Variable Order

2023
The aim of this paper is to present an approximation formula for the Caputo fractional derivative of variable order, with dependence on an arbitrary kernel. For special cases of this kernel function, or the fractional order being constant, we recover some known formulas.
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Fractional derivatives: integral representations and generalized polynomials

2004
Summary: We show that the use of functions associated with generalized forms of Hermite polynomials provide a natural tool for the solution of partial differential equations involving fractional derivatives. Within such a context we clarify the meaning of exponential operators with fractional derivatives and discuss alternative definitions based on ...
DATTOLI G +3 more
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On Some Generalizations of the Bi-Ordinal Hilfer’s Fractional Derivative

Cybernetics and Systems Analysis
The article is devoted to the generalization of the concept of bi-ordinal Hilfer’s fractional derivative, previously introduced in an author’s work. In particular, the concept of the bi-ordinal Hilfer’s derivative of a function with respect to another function and proportional bi-ordinal Hilfer derivative of a function with respect to another function ...
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Generating Functions and Approximations of the Caputo Fractional Derivative