Barycentric Legendre interpolation method for solving nonlinear fractal-fractional Burgers equation

In this paper, we formulate a numerical method to approximate  the  solution of non-linear fractal-fractional Burgers equation. In this model, differential operators are defined in the Atangana-Riemann-Liouville sense with Mittage-Leffler kernel. We first expand the spatial derivatives using barycentric interpolation method and then we derive an operational matrix (OM) of the fractal-fractional derivative for the Legendre polynomials. To be more precise, two approximation tools are coupled to convert the fractal-fractional Burgers equation into a  system of  algebraic equations which is technically uncomplicated and can be solved using available mathematical software such as MATLAB.  To investigate the agreement between exact  and approximate solutions, several examples are examined.