Existence results for nonlocal Cauchy problem of nonlinear $\psi-$Caputo type fractional differential equations via topological degree methods

Abstract

This manuscript is devoted to the investigation of the existence results of fractional Cauchy problem forsome nonlinear ψ−Caputo fractional differential equations with non local conditions. By applying fixedpoint theorems, some results of topological degree theory for condensing maps and some fractional analysistechniques, we establish some new existence theorems. As application, a nontrivial example is given toillustrate our theoretical results.