On the $S$-asymptotically $ω$-periodic mild solutions for multi-term time fractional measure differential equations - Gou, Haide (Topological Methods in Nonlinear Analysis, 2023)
In this paper, based on regulated functions and fixedpoint theorem, a class of nonlocal problem of multi-term time-fractional measure differential equationsinvolving nonlocal conditions in Banach spaces. Firstly, we introduce the concept of $S$-asymptotically $ω$-periodic mild solution, on the premiseof by utilizing $(β,γ_k)$-resolvent family and measure functional (Henstock-Lebesgue-Stieltjes integral), the existence of$S$ -asymptotically $ω$ periodic mild solutions for the mentioned system are obtained. Finally, as the application of abstract results, the existence$S$-asymptotically $ω$-periodic mild solution for a classes of measure driven differential equation are discussed.