Fractional integral operators involving extended Mittag–Leffler function as its Kernel

Gauhar Rahman; Praveen Agarwal; Shahid Mubeen; Muhammad Arshad

doi:10.1007/s40590-017-0167-5

Fractional integral operators involving extended Mittag–Leffler function as its Kernel

Gauhar Rahman
, Praveen Agarwal
, Shahid Mubeen
, Muhammad Arshad

International Islamic University Islamabad
International College of Engineering
University of Sargodha

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

13 Scopus citations

Abstract

This paper is devoted to the study of fractional calculus with an integral and differential operators containing the following family of extended Mittag–Leffler function: Eα,βγ;c(z;p)=∑n=0∞Bp(γ+n,c-γ)(c)nB(γ,c-γ)Γ(αn+β)znn!,(z,β,γ∈C),in its kernel. Also, we further introduce a certain number of consequences of fractional integral and differential operators containing the said function in their kernels.

Original language	English
Pages (from-to)	381-392
Number of pages	12
Journal	Boletin de la Sociedad Matematica Mexicana
Volume	24
Issue number	2
DOIs	https://doi.org/10.1007/s40590-017-0167-5
State	Published - 1 Oct 2018
Externally published	Yes

Keywords

Extended Mittag–Leffler function
Fractional differential operator
Fractional integral operator
Lebesgue measurable function
Mittag–Leffler function

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10.1007/s40590-017-0167-5

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title = "Fractional integral operators involving extended Mittag–Leffler function as its Kernel",

abstract = "This paper is devoted to the study of fractional calculus with an integral and differential operators containing the following family of extended Mittag–Leffler function: Eα,βγ;c(z;p)=∑n=0∞Bp(γ+n,c-γ)(c)nB(γ,c-γ)Γ(αn+β)znn!,(z,β,γ∈C),in its kernel. Also, we further introduce a certain number of consequences of fractional integral and differential operators containing the said function in their kernels.",

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AU - Rahman, Gauhar

AU - Agarwal, Praveen

AU - Mubeen, Shahid

AU - Arshad, Muhammad

PY - 2018/10/1

Y1 - 2018/10/1

N2 - This paper is devoted to the study of fractional calculus with an integral and differential operators containing the following family of extended Mittag–Leffler function: Eα,βγ;c(z;p)=∑n=0∞Bp(γ+n,c-γ)(c)nB(γ,c-γ)Γ(αn+β)znn!,(z,β,γ∈C),in its kernel. Also, we further introduce a certain number of consequences of fractional integral and differential operators containing the said function in their kernels.

AB - This paper is devoted to the study of fractional calculus with an integral and differential operators containing the following family of extended Mittag–Leffler function: Eα,βγ;c(z;p)=∑n=0∞Bp(γ+n,c-γ)(c)nB(γ,c-γ)Γ(αn+β)znn!,(z,β,γ∈C),in its kernel. Also, we further introduce a certain number of consequences of fractional integral and differential operators containing the said function in their kernels.

KW - Extended Mittag–Leffler function

KW - Fractional differential operator

KW - Fractional integral operator

KW - Lebesgue measurable function

KW - Mittag–Leffler function

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SP - 381

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JO - Boletin de la Sociedad Matematica Mexicana

JF - Boletin de la Sociedad Matematica Mexicana

IS - 2

ER -

Fractional integral operators involving extended Mittag–Leffler function as its Kernel

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Keywords

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