Fractional derivatives are used to model the transmission of many real world problems like COVID‐19. It is always hard to find analytical solutions for such models. Thus, approximate solutions are of interest in many interesting applications. Stability theory introduces such approximate solutions using some conditions. This article is devoted to the investigation of the stability of nonlinear differential equations with Riemann‐Liouville fractional derivative. We employed a version of Banach fixed point theory to study the stability in the sense of Ulam‐Hyers‐Rassias (UHR). In the end, we provide a couple of examples to illustrate our results. In this way, we extend several earlier outcomes.