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

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