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

Author

Listed:
  • 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
    Department of Industrial Engineering, OSTİM Technical University, Ankara 06374, Türkiye)

  • 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)

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.

Suggested Citation

  • Hamid Boulares & Abdelkader Moumen & Khaireddine Fernane & Jehad Alzabut & Hicham Saber & Tariq Alraqad & Mhamed Benaissa, 2023. "On Solutions of Fractional Integrodifferential Systems Involving Ψ-Caputo Derivative and Ψ-Riemann–Liouville Fractional Integral," Mathematics, MDPI, vol. 11(6), pages 1-10, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1465-:d:1100175
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    References listed on IDEAS

    as
    1. Yang, Xiao-Jun & Machado, J.A. Tenreiro, 2017. "A new fractional operator of variable order: Application in the description of anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 276-283.
    2. Abdelkrim Salim & Jehad Alzabut & Weerawat Sudsutad & Chatthai Thaiprayoon, 2022. "On Impulsive Implicit ψ -Caputo Hybrid Fractional Differential Equations with Retardation and Anticipation," Mathematics, MDPI, vol. 10(24), pages 1-20, December.
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