Fractional Dynamics of Systems with Long-Range Space Interaction and Temporal Memory
arXiv:math-ph/0702065 · doi:10.1016/j.physa.2007.04.050
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.
30 pages, LaTeX
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- Conservation Laws and Hamilton's Equations for Systems with Long-Range Interaction and Memory
- Dynamics of the Chain of Oscillators with Long-Range Interaction: From Synchronization to Chaos
- On the Study of Chaos and Memory Effects in the Bonhoeffer-van der Pol Oscillator with a Non-Ideal Capacitor
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- Theory of Critical Phenomena with Memory
- Theory of Critical Phenomena with Long-Range Temporal Interaction
- New Types of Solutions of Non-Linear Fractional Differential Equations