Multi–dimensional solutions of space–time–fractional diffusion equations

Multi–dimensional solutions of space–time–fractional diffusion equations
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DOI：
10.1098/rspa.2001.0893
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发表时间：
2002-02
期刊：
Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
影响因子：
--
通讯作者：
A. Hanyga
A. Hanyga
中科院分区：
其他
文献类型：
--
作者：
A. Hanyga

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得到了多维各向异性时空分数阶扩散方程的积分形式的绿色函数和传播子。在抽象的沃尔泰拉方程的框架下研究了解的唯一性。传播函数的单峰性在中心对称的情况下得到了证明。从扩散到波传播的过渡进行了讨论。构造了数值算例。
Green's functions and propagators for the multi–dimensional anisotropic space–time fractional diffusion equation are obtained in integral form. Uniqueness of the solutions is studied in the framework of abstract Volterra equations. Unimodality of propagator functions is demonstrated in the centrally symmetric case. The transition from diffusion to wave propagation is discussed. Numerical examples are constructed.