Fractional dynamics of systems with long-range space interaction and temporal memory

Vasily E. Tarasov and George M. Zaslavsky

Physica A: Statistical Mechanics and its Applications, 2007, vol. 383, issue 2, 291-308

Abstract: Field equations with time and coordinate derivatives of noninteger order are derived from a 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 Schrödinger equations. As another example, dynamical equations for particle chains 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.

Keywords: Fractional derivatives; Fractional equations; Long-range interaction; Power-law memory (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:383:y:2007:i:2:p:291-308

DOI: 10.1016/j.physa.2007.04.050

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