Nonlinear Piecewise Caputo Fractional Pantograph System with Respect to Another Function

Abstract

The existence, uniqueness, and various forms of Ulam–Hyers (UH)-type stability results for nonlocal pantograph equations are developed and extended in this study within the frame of novel psi-piecewise Caputo fractional derivatives, which generalize the piecewise operators recently presented in the literature. The required results are proven using Banach’s contraction mapping and Krasnoselskii’s fixed-point theorem. Additionally, results pertaining to UH stability are obtained using traditional procedures of nonlinear functional analysis. Additionally, in light of our current findings, a more general challenge for the pantograph system is presented that includes problems similar to the one considered. We provide a pertinent example as an application to support the theoretical findings.