Exact solutions of generalized non-linear time-fractional reaction-diffusion equations with time delay

In this paper, we propose the invariant subspace approach to find exact solutions of time-fractional partial differential equations (PDEs) with time delay. An algorithmic approach of finding invariant subspaces for the generalized non-linear time-fractional reaction-diffusion equations with time delay is presented. We show that the fractional reaction-diffusion equations with time delay admit several invariant subspaces which further yields several distinct analytical solutions. We also demonstrate how to derive exact solutions for time-fractional PDEs with multiple time delays. Finally, we extend the invariant subspace method to more generalized time-fractional PDEs with non-linear terms involving time delay.