Existence of mild solutions for semilinear $\psi-$Caputo-type fractional evolution equations with nonlocal conditions in Banach spaces

The main crux of this manuscript is to establish the existence of mild solutions for a class of semilinear $\psi-$Caputo-type fractional evolution equations in Banach spaces with non-local conditions. The proofs are based on some fixed point theorems, compact semigroup and some basic concepts of $\psi-$fractional analysis. As application, a nontrivial example is given to illustrate our theoretical results.