Numerical Simulation for Generalized Time-Fractional Burgers' Equation with Three Distinct Linearization Schemes

Abstract

In the present study, we examined the effectiveness of three linearization approaches for solving the time-fractional generalized Burgers' equation using a modified version of the fractional derivative by adopting the Atangana-Baleanu Caputo derivative. A stability analysis of the linearized time-fractional Burgers' difference equation was also presented. All linearization strategies used to solve the proposed non-linear problem are unconditionally stable. To support the theory, two numerical examples are considered. Furthermore, numerical results demonstrate the comparison of linearization strategies and manifest the effectiveness of the proposed numerical scheme in three distinct ways.