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

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

2007-02-18

arxiv.org/abs/math-ph/0702065v1

Physics

Mathematical Physics

30 pages, LaTeX

Scientific paper

10.1016/j.physa.2007.04.050

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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