Solution for a fractional diffusion-wave equation defined in a bounded domain
Solution for a fractional diffusion-wave equation defined in a bounded domain
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DOI：
10.1023/a:1016539022492
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发表时间：
2002-07-01
影响因子：
5.6
通讯作者：
Agrawal, OP
中科院分区：
文献类型：
--
作者：
Agrawal, OP
给出了有界空间区域上分数阶扩散波方程的一般解。分数阶时间导数在Caputo意义下描述。利用有限正弦变换技术将分数阶微分方程从空间域变换到波数域。利用拉普拉斯变换将所得方程化为一个常代数方程。逆拉普拉斯和逆有限正弦变换用于获得所需的解决方案。响应表达式用Mittag-Leffler函数表示。对于一阶和二阶导数项，这些表达式归结为普通的扩散和波动解。两个例子来说明本技术的应用。结果表明，对于1/2阶和3/2阶分数阶时间导数，系统分别表现出慢扩散和混合扩散波行为。
A general solution is given for a fractional diffusion-wave equation defined in a bounded space domain. The fractional time derivative is described in the Caputo sense. The finite sine transform technique is used to convert a fractional differential equation from a space domain to a wavenumber domain. Laplace transform is used to reduce the resulting equation to an ordinary algebraic equation. Inverse Laplace and inverse finite sine transforms are used to obtain the desired solutions. The response expressions are written in terms of the Mittag-Leffler functions. For the first and the second derivative terms, these expressions reduce to the ordinary diffusion and wave solutions. Two examples are presented to show the application of the present technique. Results show that for fractional time derivatives of order 1/2 and 3/2, the system exhibits, respectively, slow diffusion and mixed diffusion-wave behaviors.