On Impulsive Implicit ψ-Caputo Hybrid Fractional Differential Equations with Retardation and Anticipation - Abdelkrim Salim; Jehad Alzabut; Weerawat Sudsutad; Chatthai Thaiprayoon (Mathematics, 2022)
In this paper, we investigate the existence and Ulam–Hyers–Rassias stability results for a class of boundary value problems for implicit <semantics>ψ</semantics>-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.