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A class of time fractional partial differential equations is considered, which in- cludes a time fractional diffusion equation, a time fractional reaction-diffusion equation, a time fractional advection-diffusion equation, and their corresponding integer-order partial differential equations. The fundamental solutions to the Cauchy problem in a whole-space domain and the signaling problem in a half-space domain are obtained by using Fourier- Laplace transforms and their inverse transforms. The appropriate structures of the Green functions are provided. On the other hand, the solutions in the form of a series to the initial and boundary value problems in a bounded-space domain are derived by the sine- Laplace or cosine-Laplace transforms. Two examples are presented to show applications of the present technique. 相似文献
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一类时间分数阶偏微分方程的解 总被引:2,自引:2,他引:0
考虑一类时间分数阶偏微分方程,该方程包含几种特殊情况:时间分数阶扩散方程、时间分数阶反应-扩散方程、时间分数阶对流-扩散方程以及它们各自相对应的整数阶偏微分方程. 通过Laplace-Fourier变换及其逆变换,该方程在空间全平面和半平面内的基本解可以求出,但其表达式则是通过适当的变形来求.另外,对于有限域上的初边值问题,则可由Sine(Cosine)-Laplace变换导出该方程的一种级数形式的解,并通过两个数值例子来说明该方法的有效性. 相似文献
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