In this project, we apply the combination of Elzaki transform and homotopy perturbation method (ETHPM) to solve nonlinear fractional heat -like equations and system of equations. The linear term in the equation can be solved by using Elazaki Transform Method (ETM) and the nonlinear term can be handled by using Homotopy Perturbation Method (HPM). This method is very powerful and efficient technique for solving different kinds of linear and nonlinear fractional differential equations. The benefit of the combined ELzaki transform and homotopy perturbation method is more efficient and easier to handle nonlinear partial differential equations.