A computational approach for fractional convection-diffusion equation via integral transforms

Abstract

In this paper, two efficient analytic techniques namely the homotopy analysis transform method (HATM) and homotopy perturbation Sumudu transform method (HPSTM) are implemented to give a series solution of fractional convection-diffusion equation which describes the flow of heat. These proposed techniques introduce significance in the field over the existing techniques that make them computationally very attractive for applications. Numerical solutions clearly demonstrate the reliability and efficiency of HATM and HPSTM to solve strongly nonlinear fractional problems. Keywords: Homotopy analysis transform method, Homotopy perturbation method, Sumudu transform, Laplace transform, Fractional convection-diffusion equation, ℏ-curve