# Some Applications of Fractional Equations

Source: [Some Applications of Fractional Equations](<https://www.sota2.com/research/paper/68fa25e02c2a3760193b49fe>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T11:01:41.659Z

Authors: H. Weitzner, G. M. Zaslavsky (1 and 2) \_\_INSTITUTION\_2\_\_ Courant Institute of Mathematical Sciences, New York University, (2) Department of Physics, New York University)

Published: 2002-12-09T20:07:01.000Z

## Abstract

We present two observations related to theapplication 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.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/nlin/0212024>)

[PDF](<https://arxiv.org/pdf/nlin/0212024.pdf>)