Study a class of nonlinear fractional non-autonomous evolution equations with delay

In this paper, we deal with a class of nonlinear fractional non-autonomous evolution equations with delay by using Hilfer fractional derivative, which generalized the famous Riemann-Liouville fractional derivative. Combining techniques of fractional calculus, measure of noncompactness and some fixed point theorem, we obtain new existence result of mild solutions when the associated semigroup is not compact. Furthermore, the assumptions that the nonlinear term satisfies some growth condition and noncompactness measure condition. The results obtained improve and extend some related conclusions. Finally, two examples will be presented to illustrate the main results.