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

被引：115

作者：

Kiryakova, V. ^{[1
]}

机构：

[1] Bulgarian Acad Sci, Inst Math & Informat, BU-1113 Sofia, Bulgaria

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2010年 / 59卷 / 05期

关键词：

Special functions; Fractional calculus; Generalized hypergeometric and Mittag-Leffler functions; Fractional order differential equations;

D O I：

10.1016/j.camwa.2009.08.025

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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)Psi(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. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：1885 / 1895

页数：11

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