Measure of noncompactness approach to nonlinear fractional pantograph differential equations

Abstract

The aim of this manuscript is to explore the existence and uniqueness of solutions for a class of nonlinear \( \Psi \)-Caputo fractional pantograph differential equations subject to nonlocal conditions. The proofs rely on key results in topological degree theory for condensing maps, coupled with the method of measures of noncompactness and essential tools in \( \Psi \)-fractional calculus. To support the theoretical findings, a nontrivial example is presented as an application.