  We provide explicit representations of Green's functions for general linear
fractional differential operators with {\it variable coefficients} and
Riemann-Liouvilles derivatives. We assume that all their coefficients are
continuous in $[0, \infty)$. Using the explicit representations for Green's
function, we obtain explicit representations for solution of inhomogeneous
fractional differential equation with variable coefficients of general type.
Therefore the method of Green's function, which was developed in previous
research for solution of fractional differential equation with constant
coefficients, is extended to the case of fractional differential equations with
{\it variable coefficients}.
