An Analytical Solution of Linear/Nonlinear Fractional-Order Partial Differential Equations and with New Existence and Uniqueness Conditions

Abstract

In this paper, we have adopted the two-step Adomian decomposition method (TSADM) for solving linear and nonlinear partial differential equations of fractional order and compared with the variational iteration method (VIM) and Adomian decomposition method (ADM). It is successfully applied to linear and nonlinear partial differential equations involving variable coefficients. It is shown that the TSADM is a more effective and promising method and provides an exact solution with one iteration of the problems without discretization and linearization.