The multi-index Mittag-Leffler functions as an important class of special functions of fractional calculus

Authors:
V. Kiryakova
Affiliations:
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, "Acad. G. Bontchev" Street Block 8, Sofia 1113, Bulgaria
Venue:
Computers & Mathematics with Applications
Year:
2010

Citing 2
Cited 2

Multiple (multiindex) Mittag-Leffler functions and relations to generalized fractional calculus

Journal of Computational and Applied Mathematics - Special issue on higher transcendental functions and their applications
Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)

Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)

Numerical solution of fractional differential equations with a collocation method based on Müntz polynomials

Computers & Mathematics with Applications
Fractional integro-differential calculus and its control-theoretical applications. I. Mathematical fundamentals and the problem of interpretation

Automation and Remote Control

Quantified Score

Hi-index	0.09

Visualization

Abstract

This paper is a short description of our recent results on an important class of the so-called ''Special Functions of Fractional Calculus'' (SF of FC), which became important as solutions of fractional order (or multi-order) differential and integral equations, control systems and refined mathematical models of various physical, chemical, economical, management, bioengineering phenomena. Basically, under ''SF of FC'' we mean the Wright generalized hypergeometric function "p@J"q, as a special case of the Fox H-function. We have introduced and studied the multi-index Mittag-Leffler functions as their typical representatives, including many interesting special cases that have already proven their usefulness in FC and its applications. Some new results are also presented and open problems are discussed.