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Fractional Dynamics of Systems with Long-Range Space Interaction and Temporal Memory

Vasily E. Tarasov·George M. Zaslavsky
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Abstract

Field equations with time and coordinates derivatives of noninteger order are derived from stationary action principle for the cases of power-law memory function and long-range interaction in systems. The method is applied to obtain a fractional generalization of the Ginzburg-Landau and nonlinear Schrodinger equations. As another example, dynamical equations for particles chain with power-law interaction and memory are considered in the continuous limit. The obtained fractional equations can be applied to complex media with/without random parameters or processes.

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Vasily E. Tarasov, George M. Zaslavsky. 2007-02-18. Fractional Dynamics of Systems with Long-Range Space Interaction and Temporal Memory. https://doi.org/10.1016/j.physa.2007.04.050

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