Analyzing the stability of nonlinear fractional Pantograph integrodifferential equations through Pachpatte's inequality

Abstract

For a class of boundary value problems associated with nonlinear pantograph fractional integrodifferential equations, the work focuses on proving the existence, uniqueness, and Ulam–Hyers stability of solutions. These equations use the ${\Psi}$-Caputo fractional derivative and have positive constant coefficients. The Banach contraction mapping principle, Schaefer's fixed point theorem, and Pachpatte's integral inequality are among the fundamental mathematical techniques that form the basis of the analytical framework. An appropriate practical example is provided to bolster the theoretical conclusions.