限区间上的时间分数阶电报方程的解析解

详细信息

ANALYTIC SOLUTION FOR THE TIME-FRACTIONAL TELEGRAPH EQUATION DEFINED IN A BOUNDED DOMAIN

摘要: 考虑一类时间分数阶电报方程，它是由传统的电报方程推广而来，即时间一阶、二阶导数分别用 $\alpha\in(\frac{1}{2},1], 2\alpha\in(1,2]$ 阶Caputo导数代替. 利用空间有限的sine或cosine变换及时间Laplace变换，给出了该方程有限区间上带Dirichlet和Neumann边界条件的两类初边值问题的解析解. 该解由Mittag-Leffler函数的级数形式给出.
- 分数阶电报方程 /
- Caputo分数阶导数 /
- sine（cosine）变换 /
- Laplace变换
Abstract: In this paper, we discuss the so-called time-fractional telegraph equation. It is a generalization of the classical telegraph equation in case the first- and two-order time derivatives are replaced with Caputo derivatives of order $\alpha\in(\frac{1}{2},1], 2\alpha\in(1,2]$ . By using the spatial finite sine and cosine transform, and the temporal Laplace transform, the existence of the analytic solutions of its initial-boundary problems in a boundedspace domain with Dirichlet and Neumann boundary conditions is derived. The analytic solutions are given in the form of series of the Mittag-Leffler functions.
- fractional telegraph equations /
- Caputo fractional derivative /
- sine(cosine) transform /
- Laplace transform