International Journal of Emerging Multidisciplinaries: Mathematics

Corresponding Author

Muhammad Shakil Shaiq

Document Type

Research Article

Subject Areas

Applied Mathematics and Computations


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


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.

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