The exact asymptotics of singular values of a fractional integral operator $$ I^\alpha\cdot=\intłimits^x_0{(x-y)^{\alpha-1}\over\Gamma(\alpha)}\cdot dy $$ for $1/2<\alpha$ is found. The results related to asymptotic behavior of singular values of convolution operators similar to fractional integral operator are given. We also obtained a result about the asymptotic behavior of convolution operators with logarithm-singularity.