Generalized arbitrary order Mittag-Leffler-type function and Marichev-Saigo-Maeda fractional operators

Praveen Agarwal; Maged Bin-Saad; Jihad Younis; Shilpi Jain

doi:10.1016/B978-0-44-336484-6.00021-7

Generalized arbitrary order Mittag-Leffler-type function and Marichev-Saigo-Maeda fractional operators

Praveen Agarwal
, Maged Bin-Saad
, Jihad Younis
, Shilpi Jain

Nonlinear Dynamic Research Centre (NDRC)

International College of Engineering
University of Aden
Poornima College of Engineering

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

Several fractional calculus operators have been introduced and studied. We aim to present the Marichev-Saigo-Maeda fractional calculus operators and Caputo-type Marichev-Saigo-Maeda fractional differential operators of the generalized arbitrary order Mittag-Leffler-type function. The results are represented in terms of the Hadamard product of the generalized Mittag-Leffler function Eα,βγ,δ(z) and the Fox-Wright function Ψqp(z). Corresponding special cases related to the Saigo, Erdélyi-Kober, and Riemann-Liouville fractional integral and derivative operators are also obtained.

Original language	English
Title of host publication	Extended Hypergeometric Functions and Orthogonal Polynomials
Publisher	Elsevier
Pages	189-209
Number of pages	21
ISBN (Electronic)	9780443364846
ISBN (Print)	9780443364853
DOIs	https://doi.org/10.1016/B978-0-44-336484-6.00021-7
State	Published - 1 Jan 2026

Keywords

Fox-Wright function
Mittag-Leffler function
Operators of fractional calculus

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10.1016/B978-0-44-336484-6.00021-7

Cite this

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title = "Generalized arbitrary order Mittag-Leffler-type function and Marichev-Saigo-Maeda fractional operators",

abstract = "Several fractional calculus operators have been introduced and studied. We aim to present the Marichev-Saigo-Maeda fractional calculus operators and Caputo-type Marichev-Saigo-Maeda fractional differential operators of the generalized arbitrary order Mittag-Leffler-type function. The results are represented in terms of the Hadamard product of the generalized Mittag-Leffler function Eα,βγ,δ(z) and the Fox-Wright function Ψqp(z). Corresponding special cases related to the Saigo, Erd{\'e}lyi-Kober, and Riemann-Liouville fractional integral and derivative operators are also obtained.",

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author = "Praveen Agarwal and Maged Bin-Saad and Jihad Younis and Shilpi Jain",

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doi = "10.1016/B978-0-44-336484-6.00021-7",

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TY - CHAP

T1 - Generalized arbitrary order Mittag-Leffler-type function and Marichev-Saigo-Maeda fractional operators

AU - Agarwal, Praveen

AU - Bin-Saad, Maged

AU - Younis, Jihad

AU - Jain, Shilpi

PY - 2026/1/1

Y1 - 2026/1/1

N2 - Several fractional calculus operators have been introduced and studied. We aim to present the Marichev-Saigo-Maeda fractional calculus operators and Caputo-type Marichev-Saigo-Maeda fractional differential operators of the generalized arbitrary order Mittag-Leffler-type function. The results are represented in terms of the Hadamard product of the generalized Mittag-Leffler function Eα,βγ,δ(z) and the Fox-Wright function Ψqp(z). Corresponding special cases related to the Saigo, Erdélyi-Kober, and Riemann-Liouville fractional integral and derivative operators are also obtained.

AB - Several fractional calculus operators have been introduced and studied. We aim to present the Marichev-Saigo-Maeda fractional calculus operators and Caputo-type Marichev-Saigo-Maeda fractional differential operators of the generalized arbitrary order Mittag-Leffler-type function. The results are represented in terms of the Hadamard product of the generalized Mittag-Leffler function Eα,βγ,δ(z) and the Fox-Wright function Ψqp(z). Corresponding special cases related to the Saigo, Erdélyi-Kober, and Riemann-Liouville fractional integral and derivative operators are also obtained.

KW - Fox-Wright function

KW - Mittag-Leffler function

KW - Operators of fractional calculus

UR - https://www.scopus.com/pages/publications/105032956679

U2 - 10.1016/B978-0-44-336484-6.00021-7

DO - 10.1016/B978-0-44-336484-6.00021-7

M3 - Chapter

AN - SCOPUS:105032956679

SN - 9780443364853

SP - 189

EP - 209

BT - Extended Hypergeometric Functions and Orthogonal Polynomials

PB - Elsevier

ER -

Generalized arbitrary order Mittag-Leffler-type function and Marichev-Saigo-Maeda fractional operators

Abstract

Keywords

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