On holomorphic solutions for nonlinear singular fractional differential equations

The paper concerns with a nonlinear singular fractional differential equation: tα∂αu(t,z)∂tα=F(t,z,u,∂u∂z),0<α<1, where t∈J:=[0,1]t∈J:=[0,1] and z∈U:={z∈C:∣z∣<1}z∈U:={z∈C:∣z∣<1}. The existence and the uniqueness of holomorphic solution are established.