  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.
