Method of separation of variables and exact solution of time fractional nonlinear partial differential and differential-difference equations

In this article we consider a certain class of time fractional nonlinear partial differential equations as well as partial differential-difference equations with two independent variables and with homogeneous nonlinear terms and derive their exact solutions using the method of separation of variables. More specifically, exact solutions to discrete time fractional Korteweg-de Vries (K-dV) equation, time fractional Toda-lattice equation, time fractional heat equation and time fractional nonlinear telegraph equation with variable coefficients have been derived. The analysis shows that the method of separation of variables provides an effective tool to derive exact solutions to a specific class of time fractional nonlinear differential equations with initial and boundary conditions.