分数阶反应扩散方程的H-函数解
Solutions of fractional reaction-diffusion equations in terms of the H-function
摘要：
研究了一类以Caputo导数为时间导数，Riesz-Feller分数阶导数为空间导数的统一分数阶反应扩散方程的解.该解是通过应用拉普拉斯变换和傅里叶变换以H函数的封闭形式导出的。所得结果具有一般性，包括许多作者早期研究的结果，特别是Mainardi等人（2001，2005）对时空分数阶扩散方程基本解的研究，以及Saxena等人（2006 a，b）对分数阶反应扩散方程的研究。利用Riesz-Feller导数的优点在于，含有Riesz-Feller导数的分数阶反应扩散方程的解包含了时空分数阶扩散的基本解，而时空分数阶扩散本身就是中性分数阶扩散、空间分数阶扩散和时间分数阶扩散的推广。这些特殊类型的扩散可以被解释为随时间演化的空间密度函数，并且可以用紧凑形式的H函数表示。
英文摘要：
This paper deals with the investigation of the solution of an unified fractional reaction-diffusion equation associated with the Caputo derivative as the time-derivative and Riesz-Feller fractional derivative as the space-derivative. The solution is derived by the application of the Laplace and Fourier transforms in closed form in terms of the H-function. The results derived are of general nature and include the results investigated earlier by many authors, notably by Mainardi et al. (2001, 2005) for the fundamental solution of the space-time fractional diffusion equation, and Saxena et al. (2006a, b) for fractional reaction- diffusion equations. The advantage of using Riesz-Feller derivative lies in the fact that the solution of the fractional reaction-diffusion equation containing this derivative includes the fundamental solution for space-time fractional diffusion, which itself is a generalization of neutral fractional diffusion, space-fractional diffusion, and time-fractional diffusion. These specialized types of diffusion can be interpreted as spatial probability density functions evolving in time and are expressible in terms of the H-functions in compact form.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
