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