A New Modified Analytical Approach for the Solution of Time-Fractional Convection–Diffusion Equations With Variable Coefficients - Khan, Hassan; Kumam, Poom; Hajira,; Khan, Qasim; Tchier, Fairouz; Sitthithakerngkiet, Kanokwan; Dassios, Ioannis (Frontiers in Physics, 2022)
In this article, a new modification of the Adomian decomposition method is performed for the solution fractional order Convection-Diffusion equation with variable coefficient and initial-boundary conditions. The solutions of the suggested problems are calculated for both fractional and integer orders of the problems. The series form solutions of the problems with variable coefficients have been provided for the first time. To verify and illustrate our new technique, four numerical examples are presented and solved by using proposed technique. The derived results are plotted and the dynamics are shown for both fractional and integer orders of the problems. An excellent variation among the solutions at various fractional orders are observed. It is analyzed that the new technique based on Adomian decomposition method is an accurate and effective. The present method fits both the initial and boundary conditions with double approximations simultaneously which increases the accuracy of the present method. For the first time, the present technique is used for the solutions of the problems with variable coefficients along with initial and boundary conditions. It is therefore suggested to apply the present procedure for the solutions of other problems with variable order and coefficients along with initial and boundary conditions.