Fractional integration and differentiation of the generalized arbitrary order Mittag-Leffler-type function

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

doi:10.1016/B978-0-44-336484-6.00022-9

Fractional integration and differentiation of the generalized arbitrary order Mittag-Leffler-type function

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

Nonlinear Dynamic Research Centre (NDRC)

University of Aden
International College of Engineering
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. The aim of this chapter is to present certain formulas for the Marichev-Saigo-Maeda fractional integration and differentiation involving the generalized arbitrary order Mittag-Leffler-type function. The corresponding assertions for the Saigo, Erdélyi-Kober, and Riemann-Liouville fractional operators are also deduced.

Original language	English
Title of host publication	Extended Hypergeometric Functions and Orthogonal Polynomials
Publisher	Elsevier
Pages	211-226
Number of pages	16
ISBN (Electronic)	9780443364846
ISBN (Print)	9780443364853
DOIs	https://doi.org/10.1016/B978-0-44-336484-6.00022-9
State	Published - 1 Jan 2026

Keywords

Fox-Wright function
Marichev-Saigo-Maeda operators
Mittag-Leffler function

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10.1016/B978-0-44-336484-6.00022-9

Cite this

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AU - Agarwal, Praveen

AU - Jain, Shilpi

PY - 2026/1/1

Y1 - 2026/1/1

N2 - Several fractional calculus operators have been introduced and studied. The aim of this chapter is to present certain formulas for the Marichev-Saigo-Maeda fractional integration and differentiation involving the generalized arbitrary order Mittag-Leffler-type function. The corresponding assertions for the Saigo, Erdélyi-Kober, and Riemann-Liouville fractional operators are also deduced.

AB - Several fractional calculus operators have been introduced and studied. The aim of this chapter is to present certain formulas for the Marichev-Saigo-Maeda fractional integration and differentiation involving the generalized arbitrary order Mittag-Leffler-type function. The corresponding assertions for the Saigo, Erdélyi-Kober, and Riemann-Liouville fractional operators are also deduced.

KW - Fox-Wright function

KW - Marichev-Saigo-Maeda operators

KW - Mittag-Leffler function

UR - https://www.scopus.com/pages/publications/105032945805

U2 - 10.1016/B978-0-44-336484-6.00022-9

DO - 10.1016/B978-0-44-336484-6.00022-9

M3 - Chapter

AN - SCOPUS:105032945805

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SP - 211

EP - 226

BT - Extended Hypergeometric Functions and Orthogonal Polynomials

PB - Elsevier

ER -

Fractional integration and differentiation of the generalized arbitrary order Mittag-Leffler-type function

Abstract

Keywords

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