Initial value problem for the $$(2+1)$$-dimensional time-fractional generalized convection–reaction–diffusion wave equation: invariant subspaces and exact solutions

This work investigates how we can extend the invariant subspace method to $$(2+1)$$ -dimensional time-fractional non-linear PDEs. More precisely, systematic study has been provided for constructing various dimensions of subspaces generalized convection–reaction–diffusion wave equation along with initial conditions first time. Additionally, special types above-mentioned are discussed through this separately such as reaction–diffusion equation, convection–diffusion and diffusion equation. Moreover, explain derive variety exact solutions underlying using obtained subspaces. Finally, PDEs time delay. Also, effectiveness applicability have illustrated cubic In addition, observe that be viewed combinations Mittag-Leffler function polynomial, exponential trigonometric type functions.