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On Impulsive Implicit ψ -Caputo Hybrid Fractional Differential Equations with Retardation and Anticipation

Author

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  • Abdelkrim Salim

    (Faculty of Technology, Hassiba Benbouali University of Chlef, P.O. Box 151, Chlef 02000, Algeria
    Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-Abbes, P.O. Box 89, Sidi Bel Abbes 22000, Algeria
    These authors contributed equally to this work.)

  • Jehad Alzabut

    (Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
    Department of Industrial Engineering, OSTİM Technical University, Ankara 06374, Türkiye
    These authors contributed equally to this work.)

  • Weerawat Sudsutad

    (Theoretical and Applied Data Integration Innovations Group, Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand
    These authors contributed equally to this work.)

  • Chatthai Thaiprayoon

    (Research Group of Theoretical and Computation in Applied Science, Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand
    These authors contributed equally to this work.)

Abstract

In this paper, we investigate the existence and Ulam–Hyers–Rassias stability results for a class of boundary value problems for implicit ψ -Caputo fractional differential equations with non-instantaneous impulses involving both retarded and advanced arguments. The results are based on the Banach contraction principle and Krasnoselskii’s fixed point theorem. In addition, the Ulam–Hyers–Rassias stability result is proved using the nonlinear functional analysis technique. Finally, illustrative examples are given to validate our main results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4821-:d:1007616
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    References listed on IDEAS

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    1. Danfeng Luo & Zhiguo Luo & Hongjun Qiu, 2020. "Existence and Hyers–Ulam Stability of Solutions for a Mixed Fractional-Order Nonlinear Delay Difference Equation with Parameters," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-12, October.
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    Cited by:

    1. 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.

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