| الوصف: |
<正>当前,对含有非整数阶导数和积分的方程的研究正引起越来越多学者的关注,这类分数阶导数和积分将广泛应用于科学和工程的各个领域.在标准扩散方程中用α(0<α≤1)阶分数阶导数替代一阶导数,用β(0<β≤2)阶分数阶导数替代二阶导数,得到空间-时间分数阶扩散方程.近年来,许多学者研究了空间-时间分数阶扩散方程,时间分数阶扩散-波动方程,时间分数阶扩散方程,空间分数阶扩散方程,时间分数阶对流-扩散方程,以及空间分数阶对流-扩散方程. ; A time fractional diffusion-reaction equation is obtained from the standard diffusion-reaction equation by replaciong the first-order derivative in time by a fractional diffusion-reaction in time of order α(0 <α≥1). In the paper, time fractional diffusion-reaction problems in half-space(for initial-value problem and mixed problem)and in whole-space(for Cauchy problem)are considered, respectively.Using Mellin and Laplace transforms,and properties of the Fox functions,the complete solutions of these time fractional diffusion-reaction problems are derived and the explicit expressions of the Green function are obtained.The general solution of this time fractional diffusion-reaction equation in a bounded space domain is also derived by using finite sine transform technique. ; 中国国家自然科学基金(10271098)． |
