Meerschaert Mark M, Benson David A, Scheffler Hans-Peter, Baeumer Boris
Department of Mathematics, University of Nevada, Reno, Nevada 89557-0084, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Apr;65(4 Pt 1):041103. doi: 10.1103/PhysRevE.65.041103. Epub 2002 Mar 28.
Classical and anomalous diffusion equations employ integer derivatives, fractional derivatives, and other pseudodifferential operators in space. In this paper we show that replacing the integer time derivative by a fractional derivative subordinates the original stochastic solution to an inverse stable subordinator process whose probability distributions are Mittag-Leffler type. This leads to explicit solutions for space-time fractional diffusion equations with multiscaling space-fractional derivatives, and additional insight into the meaning of these equations.
经典扩散方程和反常扩散方程在空间中采用整数阶导数、分数阶导数及其他伪微分算子。在本文中，我们表明用分数阶导数取代整数阶时间导数会使原随机解从属于一个逆稳定从属过程，其概率分布为米塔格 - 莱夫勒型。这导致了具有多尺度空间分数阶导数的时空分数阶扩散方程的显式解，并对这些方程的意义有了进一步的认识。
