On the $S$-asymptotically $\omega$-periodic mild solutions for multi-term time fractional measure differential equations

Abstract

In this paper, based on regulated functions and fixed point theorem, a class of nonlocal problem of multi-term time-fractional measure differential equations involving nonlocal conditions in Banach spaces. Firstly, we introduce the concept of $S$-asymptotically $\omega$-periodic mild solution, on the premise of by utilizing $(\beta,\gamma_k)$-resolvent family and measure functional (Henstock-Lebesgue-Stieltjes integral), the existence of $S$-asymptotically $\omega$ periodic mild solutions for the mentioned system are obtained. Finally, as the application of abstract results, the existence $S$-asymptotically $\omega$-periodic mild solution for a classes of measure driven differential equation are discussed.