Exact solution of certain time fractional nonlinear partial differential equations

Abstract

Given a time fractional nonlinear partial differential equation, we show how to derive its exact solution using invariant subspace method. This has been illustrated through time fractional diffusion convection equation, time fractional nonlinear dispersive Boussinesq equation, time fractional reaction diffusion equation of second order, time fractional thin-film equation, and time fractional quadratic wave equation. Also, we explicitly shown that time fractional nonlinear partial differential equations admit more than one invariant subspaces which in turn helps to derive more than one exact solution.