On the solutions of nonlinear Caputo–Fabrizio fractional partial differential equations arising in applied mathematics

This paper proposes a new semi-analytical method known as the variational iteration transform method (VITM) to obtain the solutions of the nonlinear Caputo–Fabrizio fractional partial differential equations arising in applied mathematics. For nonlinear equations in general, there is no method that gives an exact solution and, therefore, only approximate analytical solutions can be derived by using procedures such as linearization or perturbation. This method is combined form of the Aboodh transform and the variational iteration method. The advantage of VITM is the simplicity of the computations and the non-requirement of linearization or smallness assumptions. Moreover, this method enables us to overcome the difficulties arising in identifying the general Lagrange multiplier. For further illustrations of the efficiency and reliability of VITM, some numerical applications are pesented. The numerical results showed that the proposed method is efficient and precise to obtain the solutions of nonlinear fractional partial differential equations.