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Symmetry
Volume 16
Issue 8
10.3390/sym16080963
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Article

On Fractional Operators Involving the Incomplete Mittag-Leffler Matrix Function and Its Applications

by
Ahmed Bakhet
1,2,*,
Shahid Hussain
1,* and
Mohra Zayed
3,*
1
College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China
2
Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt
3
Mathematics Department, College of Science, King Khalid University, Abha 61413, Saudi Arabia
*
Authors to whom correspondence should be addressed.
Symmetry 2024, 16(8), 963; https://doi.org/10.3390/sym16080963
Submission received: 15 May 2024 / Revised: 20 June 2024 / Accepted: 26 June 2024 / Published: 29 July 2024
(This article belongs to the Special Issue Research in Special Functions)
Versions Notes

Abstract

In this study, we derive multiple incomplete matrix Mittag-Leffler (ML) functions. We systematically investigate several properties of these incomplete matrix ML functions, which include some general properties and distinct representations of integral transforms. We further study the properties of the Riemann–Liouville fractional integrals and derivatives related to the incomplete matrix ML functions. Additionally, some interesting special cases of this work are highlighted. Finally, we establish the solution to the kinetic equations as an application.
Keywords: fractional calculus operators; incomplete hypergeometric matrix function; matrix functional calculus; Mittag-Leffler functions fractional calculus operators; incomplete hypergeometric matrix function; matrix functional calculus; Mittag-Leffler functions

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MDPI and ACS Style

Bakhet, A.; Hussain, S.; Zayed, M. On Fractional Operators Involving the Incomplete Mittag-Leffler Matrix Function and Its Applications. Symmetry 2024, 16, 963. https://doi.org/10.3390/sym16080963

AMA Style

Bakhet A, Hussain S, Zayed M. On Fractional Operators Involving the Incomplete Mittag-Leffler Matrix Function and Its Applications. Symmetry. 2024; 16(8):963. https://doi.org/10.3390/sym16080963

Chicago/Turabian Style

Bakhet, Ahmed, Shahid Hussain, and Mohra Zayed. 2024. "On Fractional Operators Involving the Incomplete Mittag-Leffler Matrix Function and Its Applications" Symmetry 16, no. 8: 963. https://doi.org/10.3390/sym16080963

APA Style

Bakhet, A., Hussain, S., & Zayed, M. (2024). On Fractional Operators Involving the Incomplete Mittag-Leffler Matrix Function and Its Applications. Symmetry, 16(8), 963. https://doi.org/10.3390/sym16080963

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