Weyl型分数阶积分与一类复二阶微分方程的α-形式解

数学理论与应用 ›› 2017, Vol. 37 ›› Issue (3-4): 51-58.

Weyl型分数阶积分与一类复二阶微分方程的α-形式解

陈真超，黄斌

长沙理工大学数学与统计学院

出版日期:2017-12-30 发布日期:2020-09-21

Weyl Fractional Integral andα-form Solutions to Complex Second Order Differential Equations

Chen Zhenchao ，Huang Bing

School of Mathematics and Statistics,Changsha University of Science and Technology

Online:2017-12-30 Published:2020-09-21

摘要/Abstract

摘要：

本文给出复微分方程的α-形式解的概念,并用Weyl型分数阶积分给出形如t² z″(t)- (bt+ c)z′(t)+βz(t)=0的复微分方程的一种α-负幂解形式,进而得到这种方程有多项式解的充分必要条件.

关键词: Weyl型分数阶积分, 复微分方程, α- 形式解

Abstract: In this paper we introduce the concept ofα-form solutions to complex differential equations,andive a kind of negative powerα-form solution to the complex differential equation t² z″(t)- (bt+ c)z′(t)+βz(t)=0by employing the Weyl fractional integral,and furthermore the necessary and sufficient conditions that the equation allows a polynomial solution are concluded.

Key words:

Weyl fractional integral, Complex differential equation, α-form solution

陈真超, 黄斌.

Weyl型分数阶积分与一类复二阶微分方程的α-形式解 [J]. 数学理论与应用, 2017, 37(3-4): 51-58.

Chen Zhenchao, Huang Bing. Weyl Fractional Integral andα-form Solutions to Complex Second Order Differential Equations[J]. Mathematical Theory and Applications, 2017, 37(3-4): 51-58.