摘要翻译：
本文研究了以Caputo导数为时间导数，Riesz-Feller分数导数为空间导数的统一分数阶反应扩散方程的解。应用H-函数的Laplace变换和Fourier变换得到了该问题的解。所得到的结果是一般性的，并包括许多作者早先研究的结果，特别是Mainardi等人。(2001，2005)为时空分数阶扩散方程的基本解，以及Saxena等人。分数阶反应扩散方程(2006a，b)。采用Riesz-Feller导数的优点在于含有该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解释为随时间演化的空间概率密度函数，并可以用紧致形式的H-函数来表示。
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英文标题：
《Solutions of fractional reaction-diffusion equations in terms of the
  H-function》
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作者：
H.J. Haubold, A.M. Mathai, R.K. Saxena
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最新提交年份：
2007
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分类信息：

一级分类：Mathematics        数学
二级分类：Probability        概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Mathematics        数学
二级分类：Classical Analysis and ODEs        经典分析与颂歌
分类描述：Special functions, orthogonal polynomials, harmonic analysis, ODE's, differential relations, calculus of variations, approximations, expansions, asymptotics
特殊函数、正交多项式、调和分析、Ode、微分关系、变分法、逼近、展开、渐近
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一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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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.
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PDF链接：
https://arxiv.org/pdf/704.0329