分数阶电报方程的各种精确解析解及动力学性质

Exact-Analytic Solutions and Their Dynamical Properties of the Fractional-Order Telegraph Equation

【目的】研究3类经典的分数阶电报方程的精确求解问题。【方法】利用分离变量法与齐次平衡原理相结合的方法,并利用特殊的变换。【结果】获得了空间分数阶电报方程、时间分数阶电报方程以及时间-空间分数阶电报方程的各种精确解,进一步分析讨论了这些解的力学性质和演化现象,并给出了部分精确解随时间和空间发展演化的坐标图。【结论】与文献中的结果相比,获得的精确解大部分都是新结果,而且求解方法和技巧较之前文献中的要简便许多。

[Purposes]In order to study the exact solutions of three classes of classical fractional-order telegraph equations.[Methods]The method of the combination of the separation variable method and the homogeneous balance principle are used here.[Findings]The exact solutions of the space-fractional telegraph equation,the time-fractional telegraph equation and the time-space fractional telegraph equation are obtained by special transformation.The mechanical properties and the evolution of these solutions are further analyzed,and the graphs of partial exact solutions with time and evolution of space development is given.[Conclusions]Compared with the results in the existing literature,the exact solutions obtained here are new results,and the solving method and technique are much simpler than those in the previous literature.