Invariant subspace method for (m + 1)-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 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.
Cite
@article{arxiv.2304.02605,
title = {Invariant subspace method for (m + 1)-dimensional non-linear time-fractional partial differential equations},
author = {P. Prakash and K. S. Priyendhu and M. Lakshmanan},
journal= {arXiv preprint arXiv:2304.02605},
year = {2023}
}
Comments
49 pages