Comp. Appl. Math. https://doi.org/10.1007/s40314-018-0631-5 Discrete Hahn polynomials for numerical solution of two-dimensional variable-order fractional Rayleigh–Stokes problem Farideh Salehi 1 · Habibollah Saeedi 2,3 · Mohseni Moghadam Moghadam 1 Received: 28 January 2018 / Revised: 11 April 2018 / Accepted: 23 April 2018 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2018 Abstract The main aim of this paper is to find the numerical solutions of 2D Rayleigh–Stokes problem with the variable-order fractional derivatives in the Riemann–Liouville sense. The presented method is based on collocation procedure in combination with the new operational matrix of the variable-order fractional derivatives, in the Caputo sense, for the discrete Hahn polynomials. The main advantage of the proposed method is obtaining a global approxi- mation for spatial and temporal discretizations, and it reduced the problem to an algebraic system, which is easier to solve. Also, the profit of approximating a continuous function by Hahn polynomials is that for computing the coefficients of the expansion, we only have to compute a summation and the calculation of coefficients is exact. The error bound for the approximate solution is estimated. Finally, we evaluate results of the presented method with other numerical methods. Keywords Variable-order fractional derivatives · Two-dimensional Rayleigh–Stokes problem · Hahn polynomials · Operational matrix method Mathematics Subject Classification 26A33 · 65N35 · 35R11 · 33C45 Communicated by José Tenreiro Machado. B Habibollah Saeedi saeedi@uk.ac.ir Farideh Salehi f.salehi630@gmail.com Mohseni Moghadam Moghadam mohseni@uk.ac.ir 1 Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran 2 Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran 3 Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran 123