An Implicit Numerical Scheme Based on B-Spline Functions for Time -Fractional Burgers Equation

This paper focuses on the numerical treatment of the time-fractional Burgers equation, a significant nonlinear partial differential equation with applications in various fields such as fluid dynamics, acoustics and traffic flow. Herein, we propose an Extended Cubic B-Spline ExCBS method for approximating the solution of the time-fractional Burgers equation. The time-fractional derivative is discretized using a finite difference technique while the spatial derivatives are handled by the ExCBS method. The stability and convergence of the proposed scheme are rigorously analyzed. Numerical examples are presented to demonstrate the accuracy and efficiency of the applied method. Comparisons with existing methods in the literature illustrate the superior performance of the proposed technique for solving this class of fractional differential equations. This research offers valuable and effective numerical tool for the investigation of complex phenomena modeled by the time-fractional Burgers equation.