摘要翻译：
分数阶微积分允许人们通过用分数阶导数代替一阶时间导数或二阶空间导数来推广线性一维扩散方程。这些方程的基本解提供了随时间或空间变量演化的概率密度函数，这些函数与一类稳定分布有关。这个性质是标准扩散方程的一个值得注意的推广，可以用于处理稳定概率分布起关键作用的金融和经济问题。
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英文标题：
《Probability distributions generated by fractional diffusion equations》
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作者：
Francesco Mainardi, Paolo Paradisi and Rudolf Gorenflo
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of these equations provide probability density functions, evolving on time or variable in space, which are related to the class of stable distributions. This property is a noteworthy generalization of what happens for the standard diffusion equation and can be relevant in treating financial and economical problems where the stable probability distributions play a key role.
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PDF链接：
https://arxiv.org/pdf/704.032