University of Tabriz Computational Methods for Differential Equations 2345-3982 10 2 2022 04 01 An efficient approximate solution of Riesz fractional advection-diffusion equation 307 319 12721 10.22034/cmde.2021.41690.1815 EN Siavash Mockary Department of Mathematics, College of Science, Yadegar-e-Imam Khomeini (RAH) Shahr-e-Rey Branch, Islamic Azad University, Tehran, Iran. Alireza Vahidi Department of Mathematics, College of Science, Yadegar-e-Imam Khomeini (RAH) Shahr-e-Rey Branch, Islamic Azad University, Tehran, Iran. Esmail Babolian Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran. Journal Article 2020 09 25 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. https://cmde.tabrizu.ac.ir/article_12721_1cb3cc01abce405e339fc8c370263ba6.pdf