Theoretical and numerical aspects for the longtime behavior of nonlinear delay time Caputo fractional reaction–diffusion equations

In this paper, we investigate the longtime behavior of time fractional reaction–diffusion equations with delay. The governing partial differential equation generalizes Hutchinson, Mackey–Glass and Nicholson’s blowflies equations. Energy estimates, asymptotic stability contractivity problem are proved. finite difference technique is used to discretize time-fractional Caputo derivative, spectral Galerkin approach for spatial approximation. Additionally, ability preserve rates can be proved numerical solution similarly as true solution. Finally, some experiments performed confirm our findings.