Exact solution of nonlinear time-fractional reaction-diffusion-convection equation via a new coupling method

The main aim of this work is to find the exact solution in the form of the Mittag-Leller function for the nonlinear time-fractional reaction-diffusion-convection equation via a new coupling method namely, the Aboodh variational iteration method (AVIM). The proposed method is a coupling of the Aboodh transform method with the variational iteration method and the fractional derivative defined with the Liouville-Caputo operator. Three different numerical applications are given to demonstrate the validity and applicability of the proposed method and compare it to existing methods. The results shown through figures and tables demonstrate the accuracy of our method. It is concluded here that the proposed method is very efficient, simple and can be applied to other nonlinear problems arising in science and engineering.