On inverse problem for linear and semilinear diffusion equation with Caputo–Fabrizio derivative

Abstract

We investigate a fractional time diffusion equation with Caputo–Fabrizio derivative instead of classical derivative. We set up the existence, uniqueness, and regularity of the mild solution and then consider the above problem in some various cases including linear and nonlinear source function. Thanks to applying some Sobolev embeddings, we derive the regularity of the mild solution for linear case. For nonlinear case, we apply the fixed point theory to obtain the existence of the mild solution.