A New Modified Analytical Approach for the Solution of Time-Fractional Convection–Diffusion Equations With Variable Coefficients

Abstract

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 of 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 the 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 is observed. It is analyzed that the new technique based on the Adomian decomposition method is 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.

Distinctive Shape Functions of Fractional Differential Quadrature for Solving Two-Dimensional Space Fractional Diffusion Problems

“…Mirza et al [5] solved the time-fractionalized advection-diffusion equation by exploiting the Atangana-Baleanu fractional derivative operator. Khan et al [6] performed a new modification of the Adomian decomposition method to solve the fractional convection-diffusion equation. Attar et al [7] proposed an analytical method called Akbari-Ganji's technique for solving nonlinear fractional differential equations.…”