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

Abdelkrim Salim, Jehad Alzabut, Weerawat Sudsutad and Chatthai Thaiprayoon ()
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Abdelkrim Salim: Faculty of Technology, Hassiba Benbouali University of Chlef, P.O. Box 151, Chlef 02000, Algeria
Jehad Alzabut: Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
Weerawat Sudsutad: Theoretical and Applied Data Integration Innovations Group, Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand
Chatthai Thaiprayoon: Research Group of Theoretical and Computation in Applied Science, Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand

Mathematics, 2022, vol. 10, issue 24, 1-20

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.

Keywords: fixed point theorem; ?-Caputo fractional derivative; existence and uniqueness; Ulam–Hyers–Rassias stability; non-instantaneous impulses (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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