The fractional view analysis of the Navier-Stokes equations within Caputo operator

Chaos, Solitons & Fractals: X

Said Ahmed¹  Qasim Khan²  Fairouz Tchier³  Hassan Khan⁴  Poom Kumam⁴  Gurpreet Singh⁴  Hajira⁵  Kanokwan Sitthithakerngkiet⁶ 

[1] Corresponding author.;Department of Mathematics, Near East University TRNC, Mersin 10, Turkey;Theoretical and Computational Science (TaCS) Center, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology, Thonburi (KMUTT), Bangkok, Thailand;Department of Mathematics, Abdul Wali khan Uniuersity Mardan, Pakistan;Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan;Mathematics Department, King Saud University, Riyadh, Saudi Arabia;

关键词: Residual power series method;    Caputo derivative;    Initial-value problems;    Fractional Navier-Stokes equations;   

DOI  :  

来源: DOAJ

【 摘 要 】

In this research article the residual power series method is implemented for the solution of the Navier-stokes equations with two and three dimensions having the initial conditions. Caputo operator is used for the fractional derivative. The formulation is made in general form and then applied to the specific problems to check the validity of the suggested method. The solution of some numerical examples of the Navier-stokes equations are presented for both fractional and integer orders of the problems. The comparison of the obtained and exact solution is provided by using 2D and 3D plots of the solutions which confirmed the higher accuracy of the proposed method. Tables are drawn to show the results obtained, exact solutions and absolute error of the suggested method for each problem. It is investigated that as the number of terms increase in the series solution of the problems, the obtained solutions have the closed contact with actual solutions of each problem. From the calculated values it is cleared that the method is accurate and easy and therefore can be extended further to linear and nonlinear problems.

【 授权许可】

Unknown