作　　者： ; ;

机构地区： 华南理工大学理学院数学与应用数学系

出　　处： 《应用数学和力学》 2010年第7期781-790,共10页

摘　　要： 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. A class of time fractional partial differential equation,including time fractional diffusion equation,time fractional reaction-diffusion equation,time fractional advection-diffusion equation and their corresponding integer-order partial differential equations,was considered.The fundamental solutions for the Cauchy problem in a whole-space domain and signaling problem in a half-space domain were obtained by using Fourier-Laplace transforms and their inverse transforms.The appropriate structures for the Green functions were provided.On the other hand,the solutions in the form of a series for the initial and boundary value problems in a bounded-space domain were derived by the Sine-Laplace or Cosine-Laplace transforms.Two examples were presented to show the application of the present technique.

关 键 词： 分数阶微分方程 分数阶导数 函数 变换 变换 变换

领　　域： [理学] [理学]