【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,进而得到这种方程有多项式解的充分必要条件.更多还原

【Abstract】 In this paper we introduce the concept ofα-form solutions to complex differential equations,and give a kind of negative powerα-form solution to the complex differential equation t~2 z″(t)-(bt+c)z′(t)+βz(t)=0 by employing the Weyl fractional integral,and furthermore the necessary and sufficient conditions that the equation allows a polynomial solution are concluded.更多还原