1 deal with the stochastic process with either Volterra or Harmonizable representation
2 select any type of stochastic calculus to solve your SODE
3 (for numerical simulation) you may need to involve some special orthogonal series to approach
4 discretize the SODE and solve in either integral or differential form
Simply, the main different between Bm and fBm is the smoothness of the trajectory (we also interpret as the accelerate/decelerate regon which the particle jump into)
If you just want a quick, there is a inbuild function to generate fBm called "wfbm"
For any mistake/misunderstanding, feel free to correct me
wm
