A Gronwall lemma approach to the stability of Riemann-Liouville fractional semilinear evolution equations

Abstract

In this paper, we investigate the Hyers–Ulam and Hyers–Ulam– Rassias stability of the Riemann-Liouville fractional semilinear evolution equations. By applying a Gronwall lemma method and modifying a technique widely used in similar problems, we prove some results on this problem. We also provide an example with a graph that illustrates the improvement of the mentioned results.