Applications of the measure of noncompactness for solving nonlinear fractional pantograph differential equations

Abstract

The aim of this manuscript is to study the existence and uniqueness of solutions for a certain type of nonlinear $\Psi-$Caputo fractional pantograph differential equations with nonlocal conditions. The proofs are based on some results of topological degree theory for condensing maps combined with the technique of measures of noncompactness and certain fundamental $\Psi-$fractional calculus tools. As an application, a nontrivial example is given to illustrate our theoretical results