About the Fractal Navier–Stokes Equations
Golmankhaneh A.K. Myrzakulov R. Li S.
2025Springer Science and Business Media Deutschland GmbH
Iranian Journal of Science
2025
This paper presents a novel formulation of the Navier–Stokes equations within a fractal space-time framework by incorporating the -derivative to model fluid behavior in media with non-integer spatial and temporal dimensions. We derive the generalized fractal Navier–Stokes momentum equation and introduce a corresponding fractal Reynolds number that captures the effects of both spatial fractal dimension and temporal fractal dimension. Analytical solutions are obtained for several classical flow problems adapted to fractal geometries, including fractal Poiseuille flow, planar and generalized Couette flow, and their multi-dimensional extensions. The results reveal that increasing leads to nonlinear distortions in velocity profiles, while increasing alters the relaxation time and can induce temporal instabilities. Graphical illustrations are provided to demonstrate the influence of fractal dimensions on flow characteristics, offering new insight into the behavior of fluids in complex fractal environments.
Fractal calculus , Fractal Couette flow , Fractal differential equation , Fractal Navier–Stokes equation , Fractal Poiseuille flow
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Department of Physics, Urmia Branch, Islamic Azad University, West Azerbaijan, Urmia, Iran
Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van, Turkey
Eurasian International Centre for Theoretical Physics and Department of General, Eurasian National University, Astana, Kazakhstan
Department of Education, Kansas State University, Topeka, KS, United States
Department of Physics
Department of Mathematics
Eurasian International Centre for Theoretical Physics and Department of General
Department of Education
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