分数阶反应扩散方程
Fractional reaction-diffusion equations
摘要：
Saxena，Mathai，and Haubold（2002，2004 a，2004 b）在一系列的论文中，用广义Mittag-Leffler函数推导出了一些分数阶动力学方程的解，这是Haubold和Mathai（1995，2000）工作的扩展。本文研究一类分数阶反应扩散方程的解。所得结果具有一般性质，包括许多作者早先报道的结果，特别是Jespersen，Metzler和Fogedby（1999）对反常扩散的结果，以及del-Castillo-Negrete，Carreras和Lynch（2003）对具有Lévy飞行的反应扩散系统的结果。借助于拉普拉斯变换和傅里叶变换，我们得到了H函数的解。所得到的结果大多是适合于数值计算的形式。
英文摘要：
In a series of papers, Saxena, Mathai, and Haubold (2002, 2004a, 2004b) derived solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which provide the extension of the work of Haubold and Mathai (1995, 2000). The subject of the present paper is to investigate the solution of a fractional reaction-diffusion equation. The results derived are of general nature and include the results reported earlier by many authors, notably by Jespersen, Metzler, and Fogedby (1999) for anomalous diffusion and del-Castillo-Negrete, Carreras, and Lynch (2003) for reaction-diffusion systems with Lévy flights. The solution has been developed in terms of the H-function in a compact form with the help of Laplace and Fourier transforms. Most of the results obtained are in a form suitable for numerical computation.
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