A NUMERICAL SOLUTION FOR THE FRACTIONAL RAYLEIGH-STOKES ‎PROBLEM BY SPACE-TIME RADIAL BASIS FUNCTIONS

Subject Areas : Statistics

Nafiseh  Noghrei ¹ (Department of Applied Mathematics‎, ‎School of Mathematical Sciences‎, ‎Ferdowsi University of Mashhad‎, ‎Mashhad‎, ‎Iran.)
Asghar  Kerayechian ² (Department of Applied Mathematics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran)
Alireza  Soheili ³ (Department of Mathematics, Faculty of Mathematics, Ferdowsi University of Mashhad, Iran.)

Received: 2020-01-24 Accepted : 2020-10-14 Published : 2021-09-23

Keywords: فرمول‌بندی مکان- زمان, حسابان کسری, تابع پایه شعاعی گاوسین, روش سینک,

Abstract :

In this paper, we approximate the solution of two-dimensional Rayleigh-Stokes problem ‎for a heated generalized second grade fluid with fractional derivatives. This approximation is ‎based on the space-time radial basis functions (RBFs) and the Sinc quadrature rule. In this ‎method, we use Gaussian radial basis function and don't distinguish between time and place ‎variables and the collocation points have both the coordinates of time and space. We use the ‎Sinc quadrature rule with single exponential transformation to approximate the integral part of ‎fractional derivatives. The chosen fractional derivatives is Riemann – Liouville.‎This method is implemented on two examples with different values of the fractional ‎derivative order. Obtained results illustrate the effectiveness of our method and sh ow that ‎one can obtain accurate results with a small number of the collocation points for the radial ‎basis function. It should be noted that all calculations in this paper have been done using ‎Mathematica software.‎

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