Open Access

ARTICLE

Analysis and Numerical Computations of the Multi-Dimensional, Time-Fractional Model of Navier-Stokes Equation with a New Integral Transformation

Yuming Chu¹, Saima Rashid², Khadija Tul Kubra², Mustafa Inc^3,4,*, Zakia Hammouch⁵, M. S. Osman^6,*

1 Department of Mathematics, Huzhou University, Huzhou, China
2 Department of Mathematics, Government College University, Faisalabad, Pakistan
3 Department of Mathematics, Firat University, Elazig, Turkey
4 Medical Research, China Medical University, Taichung, Taiwan
5 Division of Applied Mathematics, Thu Dau Mot University, Thu Dau Mot, Vietnam
6 Department of Mathematics, Faculty of Science, Cairo University, Giza, 12613, Egypt

* Corresponding Authors: Mustafa Inc. Email: ; M. S. Osman. Email: ,

(This article belongs to the Special Issue: Applications of Fractional Operators in Modeling Real-world Problems: Theory, Computation, and Applications)

Computer Modeling in Engineering & Sciences 2023, 136(3), 3025-3060. https://doi.org/10.32604/cmes.2023.025470

Received 14 July 2022; Accepted 26 October 2022; Issue published 09 March 2023

Abstract

The analytical solution of the multi-dimensional, time-fractional model of Navier-Stokes equation using the triple and quadruple Elzaki transform decomposition method is presented in this article. The aforesaid model is analyzed by employing Caputo fractional derivative. We deliberated three stimulating examples that correspond to the triple and quadruple Elzaki transform decomposition methods, respectively. The findings illustrate that the established approaches are extremely helpful in obtaining exact and approximate solutions to the problems. The exact and estimated solutions are delineated via numerical simulation. The proposed analysis indicates that the projected configuration is extremely meticulous, highly efficient, and precise in understanding the behavior of complex evolutionary problems of both fractional and integer order that classify affiliated scientific fields and technology.

---

Keywords

---