论文标题
CAUCHY问题的一般时间分数扩散方程
Cauchy problem for general time fractional diffusion equation
论文作者
论文摘要
在目前的工作中，我们考虑了Kochubei提出的一般Caputo型差异操作员的时间分数扩散方程的库奇问题。首先，通过使用傅立叶分析技术，建立了无源术语的方程解决方案解决方案的阳性和长时间行为。然后，基于使用通用操作员的非源性线性普通微分方程的解表示，研究了带有源项的扩散方程的相似问题。
In the present work, we consider the Cauchy problem for the time fractional diffusion equation involving the general Caputo-type differential operator proposed by Kochubei. First, the existence, the positivity and the long time behavior of solutions of the equation without source term are established by using the Fourier analysis technique. Then, based on the representation of the solution of the inhomogenous linear ordinary differential equation with the general operator, the similar problems for the diffusion equation with source term are studied.
