Wright函数的分析性质及其应用
Analytical properties and applications of the Wright function
摘要：
在这篇综述论文中，我们考虑了赖特函数的一些应用，特别强调了它在分数阶偏微分方程中的关键作用。结果表明，时间分数阶扩散波方程的格林函数可以用Wright函数表示。进一步将偏微分方程的李群方法推广到分数阶偏微分方程，证明了分数阶偏微分方程的某些群不变解可以用Wright函数和广义Wright函数给出，最后讨论了Wright函数的零点分布、阶、型和指示函数的最新结果.
英文摘要：
In this survey paper we consider some applications of the Wright function with special emphasis of its key role in the partial differential equations of fractional order. It was found that the Green function of the time-fractional diffusion-wave equation can be represented in terms of the Wright function. Furthermore, extending the methods of Lie groups in partial differential equations to the partial differential equations of fractional order it was shown that some of the group-invariant solutions of these equations can be given in terms of the Wright and the generalized Wright functions.Finally, we discuss recent results about distribution of zeros of the Wright function, its order, type and indicator function.
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