S-Asymptotically $$\varvec{\omega }$$ ω -Periodic Mild Solutions of Neutral Fractional Differential Equations with Finite Delay in Banach Space

Abstract

In this paper, we present some results concerning the existence and uniqueness of S-asymptotically $$\omega $$ -periodic solutions for a class of nonlinear fractional differential equations with finite delay in Banach space X. These results are new even in the case of $$X=\mathbb {R}^n$$ . Moreover, we apply the above results to study the S-asymptotically $$\omega $$ -periodicity for the fractional-order diffusion equations and the fractional-order autonomous neural networks with delay.