Exact and Approximate Solutions of Heat Fractional Differential Equation Using Laplace Residual Power Series Method

This study deals with the analytical and approximate solutions of the Heat fractional Partial differential equation under Caputo’s definition. Through a practical and highly efficient technique called Laplace residual power series method. In fact, this method is a combination of the residual power series method and the Laplace transformation. In this method, we transfer the considered equation to the Laplace space, then by the concept of the limit we construct in fast convergence a new fractional expansion of the Maclaurin series solution and finally transform back the approximate solution. The Laplace residual power series method can be used to find analytical and approximate solutions for both linear and nonlinear fractional partial differential equations.