In this talk, we will show that the classical Bloch space and the Bergman space induced by a radial doubling weight, can be characterized by using the fractional derivative induced by two radial weights admitting certain doubling conditions. The arguments employed here rely on the natural integral representation via the Bergman reproducing kernels of the Hilbert space. On the path to our main result, we also study the boundedness of fractional derivative as an integral operator from weighted L^\infty to weighted Bloch spaces. This is a joint work with A. Perälä and J. Rättyä.