The invariant subspace method for solving nonlinear fractional partial differential equations with generalized fractional derivatives

Abstract

In this paper, we show that the invariant subspace method can be successfully utilized to get exact solutions for nonlinear fractional partial differential equations with generalized fractional derivatives. Using the invariant subspace method, some exact solutions have been obtained for the time fractional Hunter-Saxton equation, a time fractional nonlinear diffusion equation, a time fractional thin-film equation, the fractional Whitman-Broer-Kaup-type equation, and a system of time fractional diffusion equations.