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. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.

Automated summary

The present paper investigates a nonlocal problem for semilinear fractional diffusion equations with Riemann-Liouville derivative. By applying Banach fixed point theorem and techniques on Mittag-Leffler functions, results on the existence, uniqueness, and regularity of mild solutions in suitable spaces are established. Additionally, the convergence of mild solutions as the parameter tends to zero is shown, and numerical examples are presented to illustrate the proposed method.