Cauchy problem with $\psi $--Caputo fractional derivative in Banach spaces

Abstract

This paper is devoted to the existence of solutions for certain classes of nonlinear differential equations involving the $\psi $--Caputo fractional derivative in Banach spaces. Our approach is based on a new fixed point theorem with respect to convex-power condensing operator combined with the technique of measures of noncompactness. Finally, two examples are given to illustrate the obtained results.