Invariant subspace method for [formula omitted]-dimensional non-linear time-fractional partial differential equations

Abstract

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 for finding a large class of various types of 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.