On the S-asymptotically ω-periodic mild solutions for multi-term time fractional measure integro-differential equations

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This paper deals with a class of nonlocal problem for multi-term time-fractional measure integro-differential evolution equations of mixed type in Hilbert spaces. Firstly, we introduce the concept of S-asymptotically ω-periodic mild solution, on the premise of by utilizing ( β , γ k ) -resolvent family and measure functional (Henstock–Lebesgue–Stieltjes integral). Secondly, combining regulated functions and fixed point theorem, the existence S-asymptotically ω-periodic mild solution for a classes of measure-driven differential equation is discussed. Finally, as samples of applications, we consider the nonlocal problem to a class of time-fractional measure partial differential equation with nonlocal condition at the end of this paper.