Numerical solutions of Atangana-Baleanu time-fractional advection diffusion equation via an extended cubic B-spline technique

Abstract

The B-spline function is made up of a set of smooth piecewise polynomials that are controlled by a set of control points. A linear combination of B-spline basis of a particular degree can be used to express any spline function of that degree. The spline functions and their derivatives are continuous and depending on the multiplication of knots. In this study, an extended cubic B-spline (ECBS) approximation is used for the numerical solution of time-fractional advection diffusion equation (TFADE) involving Atangana-Baleanu fractional derivative (ABFD). Initially, the non-singular kernel ABFD is discretized using finite difference method (FDM). The spatial derivatives are discretized using ECBS functions. Convergence and stability of the proposed scheme are studied. The results tabulated in tables that show how they accurate and desirable the outcomes are by comparing the obtained approximate results with the available exact solutions. To the authors’ knowledge, this work is the first time to use the ABFD for numerical solution of time-fractional advection diffusion equation using ECBS.

Keywords

• Time fractional Atangana-Baleanu derivative
• TFADE
• ECBS functions
• FDM
• Stability and convergence