In this research work, the numerical scheme for obtaining the linear time-fractional differential equations was considered and the nature of these time-fractional differential equations are in sense of Caputo. A theorem was proved to show the Kamal transform of nth order Caputo derivatives. Finally, three problems were considered regarding the linear time-fractional differential equations which presented that the convergence of the scheme provided in the research are of high accuracy for solving and linear fractional differential equations.