Some Applications of Fractional Equations
By H. Weitzner, G. S. O. Sciences, N. University, D. Physics. 2002
171 citations recorded by the source corpus.
Abstract We present two observations related to the application of linear (LFE) and nonlinear fractional equations (NFE). First, we give the comparison and estimates of the role of the fractional derivative term to the normal diffusion term in a LFE. The transition of the solution from normal to anomalous transport is demonstrated and the dominant role of the power tails in the long time asymptotics is shown. Second, wave propagation or kinetics in a nonlinear media with fractal properties is considered. A corresponding fractional generalization of the Ginzburg–Landau and nonlinear Schrodinger equations is proposed.
Subfields: Modeling and Simulation, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/ffdaef266b42c5a0e2bdb45b9e88705225995ab7
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In Modeling and Simulation
In Statistical and Nonlinear Physics
Citations in the corpus
- Recent progress in the theory of Nonlinear Diffusion with Fractional Laplacian Operators (2014, unknown): “[61, 63, 74, 73, 88, 97, 99] and their references.”
- On a Fractional Ginzburg–Landau Equation and 1/2-Harmonic Maps into Spheres (2013, unknown): “If v is a smooth bounded function, the distribution (−∆) 12 v can be rewritten from (2.6) as a pointwise defined function through the formula (−∆) 12 v(x) = p.v. ( γn ∫ Rn v(x)− v(y) |x− y|n+1 dy ) := lim δ↓0 γn ∫ Rn\Dδ(x) v(x)− v(y) |x− y|n+1 dy .”
- Time-space fabric underlying anomalous diffusion (2005, methodology): “In the literature [20–24], the above fractional Schrödinger equation (11) were derived either based on the quantum integral over the Lévy paths in contrast to the conventional Feynman Gaussian path integral [20,21] or the fractional time derivative representation of the fractional Brownian motion [2”