Invariant subspace method for two-coupled time-fractional nonlinear partial differential equations of third-order

In this paper, we extend the invariant subspace method to coupled fractional higher order nonlinear partial differential equations. In particular, we consider a two coupled fractional partial differential equations of the form [Formula: see text] where [Formula: see text], [Formula: see text] are third-order nonlinear differential operators with quadratic nonlinearities and study the four-dimensional subspaces admitted by them. Using the obtained invariant subspaces we find explicit solutions to many two coupled fractional partial differential equations including the time-fractional equivalent of potential Korteweg–de Vries equation, reduced Super Korteweg–de Vries equation, supersymmetric extension of Korteweg–de Vries equation and generalized Drinfeld–Sokolov equation.