On a class of non-linear delay distributed order fractional diffusion equations

In this paper, we consider a numerical scheme for a class of non-linear time delay fractional diffusion equations with distributed order in time. This study covers the unique solvability, convergence and stability of the resulted numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order O(τ+(Δα)4+h4) in L∞-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.