Regularity for a non-local diffusion equation with Riemann-Liouville derivative

Abstract

Our main goal in this paper is to investigate the regularity of the mild solution fractional diffusion equation which can be used in the modelling of heat transfer with memory effects. Under some various assumptions of the input data, we obtain two main results. We also provide the upper bound and lower bound of the source function. The main tool is to use complex evaluations involving the Wright function.