Authors : Nilam Ghadage; Soni Pathak

Volume/Issue : Volume 11 - 2026, Issue 6 - June

Google Scholar : https://tinyurl.com/3k547exp

Scribd : https://tinyurl.com/4njp2jms

DOI : https://doi.org/10.38124/ijisrt/26jun154

Note : A published paper may take 4-5 working days from the publication date to appear in PlumX Metrics, Semantic Scholar, and ResearchGate.

Abstract : The classical Navier-Stokes equations have been astronomically used to describe fluid movement in engineering and scientific operations. still, their capability to model complex marvels similar as turbulent overflows, anomalous prolixity, and multiphase transport is limited because they calculate on original relations and memoryless hypotheticals. Fractional math provides a important fine frame for incorporating temporal memory and spatial nonlocality into fluid- inflow models. This review presents a comprehensive overview of fractional Navier – Stokes equations, including their fine foundations, governing phrasings, numerical result ways, and recent operations. Particular attention is given to fractional turbulence models, anomalous transport processes, and multiphase flux systems. Numerical approaches analogous as the Variational Iteration transform Method (VITM), Hybrid Finite Difference – Finite Element Method (FDM – FEM), Residual Power Series Method( RPSM), and spectral styles are critically examined. likewise, the advantages, limitations, and unborn exploration directions of fractional fluid dynamics are bandied. The review highlights the eventuality of fractional models to ameliorate the vaticination of complex inflow gesteby landing long- range relations, memory goods, andnon-Gaussian transport mechanisms that are n't adequately represented by classical fluid models.

Keywords : Fractional Navier–Stokes Equations; Fractional Calculus; Turbulence Modeling; Fractional Laplacian; Anomalous Diffusion; Multiphase Flow; Nonlocal Transport; Numerical Methods.

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