  In this paper, we generalize the theory of the invariant subspace method to
(m + 1)-dimensional non-linear time-fractional partial differential equations
for the first time. More specifically, the applicability and efficacy of the
method have been systematically investigated through the (3 + 1)-dimensional
generalized non-linear time-fractional diffusion-convection-wave equation along
with appropriate initial conditions. This systematic investigation provides an
important technique to find a large class of various types of the invariant
subspaces with different dimensions for the above-mentioned equation.
Additionally, we have shown that the obtained invariant subspaces help to
derive a variety of exact solutions that can be expressed as the combinations
of exponential, trigonometric, polynomial and well-known Mittag-Leffler
functions.
