  In this note we consider generalized diffusion equations in which the
diffusivity coefficient is not necessarily constant in time, but instead it
solves a nonlinear fractional differential equation involving fractional
Riemann-Liouville time-derivative. Our main contribution is to highlight the
link between these generalised equations and fractional Brownian motion (fBm).
In particular, we investigate the governing equation of fBm and show that its
diffusion coefficient must satisfy an additive evolutive fractional equation.
We derive in a similar way the governing equation of the iterated fractional
Brownian motion.
