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Fractional dynamics of systems with long-range space interaction and temporal memory |
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| Authors: | Vasily E Tarasov George M Zaslavsky |
| Institution: | a Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, NY 10012, USA b Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow 119992, Russia c Department of Physics, New York University, 2-4 Washington Place, New York, NY 10003, USA |
| 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 |
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