| | | | | 空间—时间分数阶对流扩散方程的分析解及基本解的性质 | | | 郑达艺 | | | 本文考虑空间时间分数阶对流—扩散方程(即在一个标准对流—扩散方程中,用β(0<β≤1)阶导数代替时间一阶导数,用a(1 【作者单位】：福建教育学院数理系 福建福州350025
【关键词】：空间时间分数阶对流—扩散方程;Fourier变换;Laplace变换
【分类号】：O175.2
【DOI】：CNKI:SUN:FJXB.0.2007-10-029
【正文快照】：
1引言近年来在国际上兴起的分数阶导数正在物理,工程,金融及环境问题等方面得到广泛应用,分数阶微分方程能更好地拟合它们的运动和变化过程,例如,刘发旺教授用分数阶微分方程模拟地下水的运动过程比用整数阶好。对一些典型的微分方程把整数阶改为分数阶,它们怎么求解?解又如何? | | | | | |  推荐 下载CAJ全文  下载PDF全文 | | | CAJViewer7.0阅读器支持所有CNKI文件格式，AdobeReader仅支持PDF格式 | | | | The Analytic Solution and the Fundamental Solution of a Space and Time Fractional Advection-dispersion Equation | | | ZHENG Da-yi(Department of Mathematics and Physics;Fujian Institute of Education;Fuzhou 350025;China) | | | The analytic solution of a space and time fractional advection-dispersion equation is considered. This equation is obtained from an advection-dispersion equation by replacing the second order derivative in space by order derivate in space of order, the first order derivative in space by order derivative in space of order and the first order derivative at time by order derivative at time of order. Using the Fourier transform, the Laplace transform and their inverse transforms, the analytic solution of this equation can be arrived at. The fundamental solution of this equation is discussed.
【Keyword】：space and time fractional advection-dispersion equation;the Fourier transform;the Laplace transform |
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