Fractional hydrodynamic equations for fractal media

By Vasily E. Tarasov. 2005

224 citations recorded by the source corpus.

Abstract We use the fractional integrals in order to describe dynamical processes in the fractal medium. We consider the “fractional” continuous medium model for the fractal media and derive the fractional generalization of the equations of balance of mass density, momentum density, and internal energy. The fractional generalization of Navier–Stokes and Euler equations are considered. We derive the equilibrium equation for fractal media. The sound waves in the continuous medium model for fractional media are considered.

Subfields: Mechanics of Materials, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d1c5495c1f25d1faebbfe05e454f56e9e68bdcde

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In Mechanics of Materials

In Modeling and Simulation

In Statistical and Nonlinear Physics

Citations in the corpus

Review of Some Promising Fractional Physical Models (2013, background): “= c−1 3 (D,r)c2(d,r)pkl ∇luk +∇ D k qk. (57) Here D is a mass dimension of fractal medium, and d dt D = ∂ ∂t +c −1 3 (D,r)c2(d,r)ul∇l, ∇D k A = c3 (D,r)∇k(c2(d,r)A). These equations are proved in [105]. 6.3 Moment of inertia for fractal bodies The moments of inertia of fractal-homogenous rigid bal”
Fractal solids, product measures and fractional wave equations (2009, result): “Comparing the results between the mechanical and variational approaches, we find that equation (5.4b) agrees with (5.10b), while equation (5.4a) contradicts (5.10a )( Tarasov 2005b, c).”
Advanced Local Fractional Calculus and Its Applications (2012, unknown): “[178] V.”