On the solutions of certain fractional kinetic matrix equations involving Hadamard fractional integrals

Mohamed Akel; Muajebah Hidan; Salah Boulaaras; Mohamed Abdalla; Mohamed Akel; Muajebah Hidan; Salah Boulaaras; Mohamed Abdalla

doi:10.3934/math.2022850

AIMS Mathematics

2022, Volume 7, Issue 8: 15520-15531. doi: 10.3934/math.2022850

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On the solutions of certain fractional kinetic matrix equations involving Hadamard fractional integrals

1.
Mathematics Department, Faculty of Science, South Valley University, Qena 83523, Egypt
2.
Mathematics Department, Faculty of Science, King Khalid University, Abha 61471, Saudi Arabia
3.
Department of Mathematics, College of Sciences and Arts, ArRas, Qassim University, Saudi Arabia

Received: 10 April 2022 Revised: 08 June 2022 Accepted: 09 June 2022 Published: 22 June 2022
MSC : 33B15, 33C05, 33C20, 34A05

Currently, matrix fractional differential equations have several applications in diverse fields, including mathematical analysis, control systems, economics, optimization theory, physics, astrophysics and engineering. In this line of research, we introduce generalized fractional kinetic equations including extended $ k $-Hurwitz-Lerch zeta-matrix functions. By applying the Hadamard fractional integral properties and via the Mellin integral transform, we present the solution of fractional kinetic matrix equations involving families of Hurwitz-Lerch zeta matrix functions. In addition, we consider a number of specific instances of our key results.
- Hadamard fractional integral,
- fractional kinetic equations,
- Hurwitz-Lerch zeta-matrix functions
Citation: Mohamed Akel, Muajebah Hidan, Salah Boulaaras, Mohamed Abdalla. On the solutions of certain fractional kinetic matrix equations involving Hadamard fractional integrals[J]. AIMS Mathematics, 2022, 7(8): 15520-15531. doi: 10.3934/math.2022850

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Abstract

Currently, matrix fractional differential equations have several applications in diverse fields, including mathematical analysis, control systems, economics, optimization theory, physics, astrophysics and engineering. In this line of research, we introduce generalized fractional kinetic equations including extended $ k $-Hurwitz-Lerch zeta-matrix functions. By applying the Hadamard fractional integral properties and via the Mellin integral transform, we present the solution of fractional kinetic matrix equations involving families of Hurwitz-Lerch zeta matrix functions. In addition, we consider a number of specific instances of our key results.

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