On Solutions of Fractional Integrodifferential Systems Involving Ψ-Caputo Derivative and Ψ-Riemann–Liouville Fractional Integral

Hamid Boulares, Abdelkader Moumen, Khaireddine Fernane, Jehad Alzabut (), Hicham Saber, Tariq Alraqad and Mhamed Benaissa
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Hamid Boulares: Laboratory of Analysis and Control of Differential Equations “ACED”, Faculty MISM, Department of Mathematics, University of 8 May 1945 Guelma, P.O. Box 401, Guelma 24000, Algeria
Abdelkader Moumen: Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 55425, Saudi Arabia
Khaireddine Fernane: Laboratory of Analysis and Control of Differential Equations “ACED”, Faculty MISM, Department of Mathematics, University of 8 May 1945 Guelma, P.O. Box 401, Guelma 24000, Algeria
Jehad Alzabut: Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
Hicham Saber: Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 55425, Saudi Arabia
Tariq Alraqad: Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 55425, Saudi Arabia
Mhamed Benaissa: Chemical Engineering Department, College of Engineering, University of Ha’il, Ha’il 81441, Saudi Arabia

Mathematics, 2023, vol. 11, issue 6, 1-10

Abstract: In this paper, we investigate a new class of nonlinear fractional integrodifferential systems that includes the Ψ -Riemann–Liouville fractional integral term. Using the technique of upper and lower solutions, the solvability of the system is examined. We add two examples to demonstrate and validate the main result. The main results highlight crucial contributions to the general theory of fractional differential equations.

Keywords: ?-Caputo derivative; ?-Riemann–Liouville fractional integral; monotone sequences; upper and lower solutions; Arzelà–Ascoli theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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