Existence and uniqueness of mild solution of time-fractional semilinear differential equations with a nonlocal final condition

In this paper, we investigate a time-fractional semilinear differential equation with final nonlocal condition [Formula presented]. Under some assumptions, we establish the existence and uniqueness of a mild solution in some suitable spaces of continuous functions. The results are based on some fixed point theorems. Two examples are presented to illustrate our results. © 2018 Elsevier Ltd