an efficient approximate solution of riesz fractional advection-diffusion equation

the riesz fractional advection-diffusion is a result of the mechanics of chaotic dynamics. it’s of preponderant importance to solve this equation numerically. moreover, the utilization of chebyshev polynomials as a base in several mathematical equations shows the exponential rate of convergence. to this approach, we transform the interval of state space into the interval [−1, 1] × [−1, 1]. then, we use the operational matrix to discretize fractional operators. applying the resulting discretization, we obtain a linear system of equations, which leads to the numerical solution. examples show the effectiveness of the method.