An approximate analytical solution of the Navier–Stokes equations within Caputo operator and Elzaki transform decomposition method

Advances in Difference Equations

Muhammad Arif¹  Adnan Khan¹  Hassan Khan²  Dumitru Baleanu³  Poom Kumam⁴ 

[1] Department of Mathematics, Abdul Wali Khan University, 23200, Mardan, Pakistan;Department of Mathematics, Abdul Wali Khan University, 23200, Mardan, Pakistan;Depatment of Mathematics, Near East University TRNC, 10, Mersin, Turkey;Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530, Ankara, Turkey;Institute of Space Sciences, Magurele-Bucharest, Romania;Theoretical and Computational Science (TaCS) Center Department of Mathematics, Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, 10140, Bangkok, Thailand;Department of Medical Research, China Medical University Hospital, China Medical University, 40402, Taichung, Taiwan;

关键词: Elzaki transformation;    Adomian decomposition method;    Navier–Stokes equations;    Caputo operator;   

DOI  :  10.1186/s13662-020-03058-1

来源: Springer

【 摘 要 】

In this article, a hybrid technique of Elzaki transformation and decomposition method is used to solve the Navier–Stokes equations with a Caputo fractional derivative. The numerical simulations and examples are presented to show the validity of the suggested method. The solutions are determined for the problems of both fractional and integer orders by a simple and straightforward procedure. The obtained results are shown and explained through graphs and tables. It is observed that the derived results are very close to the actual solutions of the problems. The fractional solutions are of special interest and have a strong relation with the solution at the integer order of the problems. The numerical examples in this paper are nonlinear and thus handle its solutions in a sophisticated manner. It is believed that this work will make it easy to study the nonlinear dynamics, arising in different areas of research and innovation. Therefore, the current method can be extended for the solution of other higher-order nonlinear problems.

【 授权许可】

CC BY