Modified Mittag-Leffler Functions with Applications in Complex Formulae for Fractional Calculus

被引：9

作者：

Fernandez, Arran ^{[1
]}

Husain, Iftikhar ^{[2
]}

机构：

[1] Eastern Mediterranean Univ, Fac Arts & Sci, Dept Math, Via Mersin 10, TR-99628 Famagusta, Northern Cyprus, Turkey

[2] Jamia Millia Islamia, Univ Polytech, Dept Appl Sci & Humanities, New Delhi 110025, India

来源：

FRACTAL AND FRACTIONAL | 2020年 / 4卷 / 03期

关键词：

Mittag-Leffler functions; Prabhakar fractional calculus; Atangana-Baleanu fractional calculus; complex integrals; analytic continuation; ASYMPTOTIC-BEHAVIOR; OPERATORS; REPRESENTATIONS; DERIVATIVES;

D O I：

10.3390/fractalfract4030045

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Mittag-Leffler functions and their variations are a popular topic of study at the present time, mostly due to their applications in fractional calculus and fractional differential equations. Here we propose a modification of the usual Mittag-Leffler functions of one, two, or three parameters, which is ideally suited for extending certain fractional-calculus operators into the complex plane. Complex analysis has been underused in combination with fractional calculus, especially with newly developed operators like those with Mittag-Leffler kernels. Here we show the natural analytic continuations of these operators using the modified Mittag-Leffler functions defined in this paper.

引用

页码：1 / 15

页数：15

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