Weyl型分数阶积分与一类复二阶微分方程的α-形式解  

Weyl Fractional Integral and form Solutions of Complex Second Order Differential Equations

作　　者：陈真超 黄斌 CHEN Zhen-chao;HUANG Bin(School of Mmathematics and Statistics,Changsha University of Science and Technology, Changsha, Hunan 41011)

机构地区：[1]长沙理工大学数学与统计学院,湖南长沙410114

出　　处：《怀化学院学报》2018年第5期18-21,共4页Journal of Huaihua University

摘　　要：给出微分方程的α-正幂解和α-形式解的概念,并用Weyl型分数阶积分给出形如t^2z″(t)-(bt+c)z′(t)+βz(t)=0的复微分方程的一种α-负幂解形式,进而还得到了这种方程有多项式解的充分必要条件.In this paper, the concept of form solutions of complex differential equations is presented, and particularly a kind of α-form solution of the differential equation of the form t^2z″（t）-（bt＋c）z′（t）＋βz（t）=0 is obtained by Weyl fractional integral. Further more, the necessary and sufficient conditions of the equation of this form possessing a polynomial solution are concluded.

关 键 词：Weyl型分数阶积分 微分方程 α-形式解 

分 类 号：O175[理学—数学]