Fractional calculus operators of special functions? The result is well predictable!

DOI10.1016/j.chaos.2017.03.006zbMath1374.26017OpenAlexW2600169063MaRDI QIDQ1677742

Virginia S. Kiryakova

Publication date: 13 November 2017

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2017.03.006

zbMATH Keywords

special functionsgeneralized hypergeometric functionsfractional calculus operatorsintegral transforms of special functions

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Mittag-Leffler functions and generalizations (33E12) Integral transforms of special functions (44A20) Hypergeometric integrals and functions defined by them ((E), (G), (H) and (I) functions) (33C60)

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Fractional order of Legendre-type matrix polynomials, New generalized mean square stochastic fractional operators with applications, Generalized derivatives and Laplace transform in (k,ψ)‐Hilfer form, Reflection properties of zeta related functions in terms of fractional derivatives, Study on Hilfer-Katugampola fractional implicit differential equations with nonlocal conditions, Optimal control of linear systems of arbitrary fractional order, On solutions of linear fractional differential equations and systems thereof, The probabilistic point of view on the generalized fractional partial differential equations, Use of fractional calculus to evaluate some improper integrals of special functions

Cites Work

• Certain fractional integral operators and the generalized multi-index Mittag-Leffler functions
• The multi-index Mittag-Leffler functions as an important class of special functions of fractional calculus
• The special functions of fractional calculus as generalized fractional calculus operators of some basic functions
• Multiple (multiindex) Mittag-Leffler functions and relations to generalized fractional calculus
• Marichev-Saigo-Maeda fractional integration operators involving generalized Bessel functions
• Fractional calculus: quo vadimus? (where are we going?)
• Multi-parametric Mittag-Leffler functions and their extension
• The Mellin integral transform in fractional calculus
• Fractional calculus: D'où venons-nous? Que sommes-nous? Où allons-nous? (Contributions to Round Table Discussion held at ICFDA 2016)
• From Bessel to Multi-Index Mittag–Leffler Functions
• Generalized fractional integration of Bessel function of the first kind
• Fractional Derivatives and Special Functions
• All the special functions are fractional differintegrals of elementary functions
• Mittag-Leffler Functions, Related Topics and Applications
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