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

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

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

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

Nonlinear Dynamic Research Centre (NDRC)

University of Aden
International College of Engineering
Poornima College of Engineering
Baku Engineering University

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

Abstract

Several fractional calculus operators have been introduced and studied. The aim of this paper 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
Pages (from-to)	1299-1313
Number of pages	15
Journal	Mathematics in Engineering, Science and Aerospace
Volume	16
Issue number	4
State	Published - 28 Nov 2025

Keywords

26A33
33B15
33E12
Fox-Wright function
Marichev-Saigo-Maeda operators
Mittag-Leffler function

Cite this

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title = "Fractional integration and differentiation of the generalized arbitrary order Mittag-Leffler-type function",

abstract = "Several fractional calculus operators have been introduced and studied. The aim of this paper 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, Erd{\'e}lyi-Kober and Riemann-Liouville fractional operators are also deduced.",

keywords = "26A33, 33B15, 33E12, Fox-Wright function, Marichev-Saigo-Maeda operators, Mittag-Leffler function",

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

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T1 - Fractional integration and differentiation of the generalized arbitrary order Mittag-Leffler-type function

AU - Bin-Saad, Maged

AU - Younis, Jihad

AU - Agarwal, Praveen

AU - Jain, Shilpi

AU - Efendiev, Rakib

N1 - Publisher Copyright: © CSP - Cambridge, UK; I&S - Florida, USA, 2025

PY - 2025/11/28

Y1 - 2025/11/28

N2 - Several fractional calculus operators have been introduced and studied. The aim of this paper 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 paper 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 - 26A33

KW - 33B15

KW - 33E12

KW - Fox-Wright function

KW - Marichev-Saigo-Maeda operators

KW - Mittag-Leffler function

UR - https://www.scopus.com/pages/publications/105023582364

M3 - Article

AN - SCOPUS:105023582364

SN - 2041-3165

VL - 16

SP - 1299

EP - 1313

JO - Mathematics in Engineering, Science and Aerospace

JF - Mathematics in Engineering, Science and Aerospace

IS - 4

ER -

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

Abstract

Keywords

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