Saichev Alexander I., Zaslavsky George M.
Radiophysics Department, Nizhniy Novgorod State University, 23 Gagarin Str., Nizhniy Novgorod, 603600, Russia.
Chaos. 1997 Dec;7(4):753-764. doi: 10.1063/1.166272.
Fractional generalization of the diffusion equation includes fractional derivatives with respect to time and coordinate. It had been introduced to describe anomalous kinetics of simple dynamical systems with chaotic motion. We consider a symmetrized fractional diffusion equation with a source and find different asymptotic solutions applying a method which is similar to the method of separation of variables. The method has a clear physical interpretation presenting the solution in a form of decomposition of the process of fractal Brownian motion and Levy-type process. Fractional generalization of the Kolmogorov-Feller equation is introduced and its solutions are analyzed. (c) 1997 American Institute of Physics.
扩散方程的分数阶推广包含关于时间和坐标的分数阶导数。它已被引入用于描述具有混沌运动的简单动力系统的反常动力学。我们考虑一个带有源项的对称分数阶扩散方程，并应用一种类似于变量分离法的方法找到不同的渐近解。该方法具有清晰的物理解释，将解表示为分形布朗运动过程和列维型过程分解的形式。引入了柯尔莫哥洛夫 - 费勒方程的分数阶推广并分析了其解。（c）1997美国物理研究所。
