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 u(x, T) - (Gu)(x) = Sigma(m)(j=1) theta(j)u(x, t(j)). 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. (C) 2018 Elsevier Ltd. All rights reserved.