具有长程空间相互作用和时间记忆系统的分数阶动力学
Fractional Dynamics of Systems with Long-Range Space Interaction and Temporal Memory
摘要：
本文从定态作用量原理出发，导出了系统中具有幂律记忆函数和长程相互作用的非整数阶时间导数和坐标导数的场方程。该方法被应用到获得一个分数推广的Ginzburg-Landau和非线性薛定谔方程。作为另一个例子，在连续极限下考虑了具有记忆和幂律相互作用的粒子链的动力学方程。所得到的分数阶方程可以应用于有无随机参数或过程的复杂介质。
英文摘要：
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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