Time-Fractional Navier-Stokes Equation Solved by Fractional Variation of Parameters Method: An Analytic Approach

Authors

Muhammad Shakil Shaiq, Department of Mathematics, The Sahara University, Narowal, 51600 PakistanFollow
Shoaib Ali, Department of Basic Sciences, University of Engineering and Technology, Taxila, 47050, PakistanFollow
Azeem Shahzad, Department of Basic Sciences, University of Engineering and Technology, Taxila, 47050, PakistanFollow
Tahir Naseem, Government Degree College Khanpur, Haripur, 22650, PakistanFollow

Corresponding Author

Muhammad Shakil Shaiq

Document Type

Research Article

Subject Areas

Applied Mathematics and Computations

Keywords

Caputo fractional derivative, Fractional calculus, Nonlinear problems, Nonlinear time-fractional Navier-Stokes Equation, Variation of Parameter Method

Abstract

In this investigation, we make use of the Variation of Parameters Method (VPM) to find a solution to the nonlinear time-fractional Navier-Stokes equation. Additionally, the fractional derivative in the sense of Riemann-Liouville is presented and discussed. Within the scope of this investigation, the Variation of Parameters Method (VPM) has been modified to include a fractional multiplier. The Fractional Variation of Parameters Method (FVPM) was created as an iterative way to solve the time-fractional nonlinear time-fractional Navier-Stokes equation. According to the findings of the calculations, the newly developed algorithm (FVPM) is compatible, accurate, and reliable.

How to Cite This Article

Shaiq, Muhammad Shakil; Ali, Shoaib; Shahzad, Azeem; and Naseem, Tahir (2023) "Time-Fractional Navier-Stokes Equation Solved by Fractional Variation of Parameters Method: An Analytic Approach," International Journal of Emerging Multidisciplinaries: Mathematics: Vol. 2: Iss. 1, Article 9.
DOI: https://doi.org/10.59790/2790-3257.1039

Receive Date

07-27-2023

Accept Date

09-05-2023

Publication Date

9-16-2023