On a semilinear fractional reaction-diffusion equation with nonlocal conditions

In the present paper, a nonlocal problem for semilinear fractional diffusion equations with Riemann-Liouville derivative is investigated. By applying Banach fixed point theorem combined with some techniques on Mittag-Leffler functions, we establish some results on the existence, uniqueness, and regularity of the mild solutions of our problem in some suitable spaces. In addition, we show that the convergence of mild solution as the parameter tends to zero and present some numerical examples to illustrate the proposed method.