Stability of fractional order of time nonlinear fractional diffusion equation with Riemann–Liouville derivative

In this paper, we investigate an equation of nonlinear fractional diffusion with the derivative of Riemann–Liouville. Firstly, we determine the global existence and uniqueness of the mild solution. Next, under some assumptions on the input data, we discuss continuity with regard to the fractional derivative order for the time. Our key idea is to combine the theories Mittag–Leffler functions and Banach fixed-point theorem. Finally, we present some examples to test the proposed theory.