Fractional differential equations for the generalized Mittag-Leffler function

Praveen Agarwal; Qasem Al-Mdallal; Yeol Je Cho; Shilpi Jain

doi:10.1186/s13662-018-1500-7

Fractional differential equations for the generalized Mittag-Leffler function

Praveen Agarwal
, Qasem Al-Mdallal
, Yeol Je Cho
, Shilpi Jain

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

80 Citations (Scopus)

Abstract

In this paper, we establish some (presumably new) differential equation formulas for the extended Mittag-Leffler-type function by using the Saigo-Maeda fractional differential operators involving the Appell function F₃(⋅) and results in terms of the Wright generalized hypergeometric-type function ψn+1({κl}l∈N0)m+1(z;p) recently established by Agarwal. Some interesting special cases are also pointed out.

Original language	English
Article number	58
Journal	Advances in Difference Equations
Volume	2018
Issue number	1
DOIs	https://doi.org/10.1186/s13662-018-1500-7
Publication status	Published - Dec 1 2018

Keywords

fractional derivative operators
generalized Gamma function
generalized Mittag-Leffler function
generalized Wright hypergeometric function
generalized beta functions

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Applied Mathematics

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10.1186/s13662-018-1500-7

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abstract = "In this paper, we establish some (presumably new) differential equation formulas for the extended Mittag-Leffler-type function by using the Saigo-Maeda fractional differential operators involving the Appell function F3(⋅) and results in terms of the Wright generalized hypergeometric-type function ψn+1(\{κl\}l∈N0)m+1(z;p) recently established by Agarwal. Some interesting special cases are also pointed out.",

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AU - Agarwal, Praveen

AU - Al-Mdallal, Qasem

AU - Cho, Yeol Je

AU - Jain, Shilpi

PY - 2018/12/1

Y1 - 2018/12/1

N2 - In this paper, we establish some (presumably new) differential equation formulas for the extended Mittag-Leffler-type function by using the Saigo-Maeda fractional differential operators involving the Appell function F3(⋅) and results in terms of the Wright generalized hypergeometric-type function ψn+1({κl}l∈N0)m+1(z;p) recently established by Agarwal. Some interesting special cases are also pointed out.

AB - In this paper, we establish some (presumably new) differential equation formulas for the extended Mittag-Leffler-type function by using the Saigo-Maeda fractional differential operators involving the Appell function F3(⋅) and results in terms of the Wright generalized hypergeometric-type function ψn+1({κl}l∈N0)m+1(z;p) recently established by Agarwal. Some interesting special cases are also pointed out.

KW - fractional derivative operators

KW - generalized Gamma function

KW - generalized Mittag-Leffler function

KW - generalized Wright hypergeometric function

KW - generalized beta functions

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JO - Advances in Difference Equations

JF - Advances in Difference Equations

IS - 1

M1 - 58

ER -

Fractional differential equations for the generalized Mittag-Leffler function

Abstract

Keywords

ASJC Scopus subject areas

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