Ortigueira, M.D.Batista, A. G.2010-01-142010-01-142008-080375-9601http://hdl.handle.net/10362/2416Physics Letters A, vol. 372; Issue 7The definition and simulation of fractional Brownian motion are considered from the point of view of a set of coherent fractional derivative definitions. To do it, two sets of fractional derivatives are considered: (a) the forward and backward and (b) the central derivatives, together with two representations: generalised difference and integral. It is shown that for these derivatives the corresponding autocorrelation functions have the same representations. The obtained results are used to define a fractional noise and, from it, the fractional Brownian motion. This is studied. The simulation problem is also considered.engForward and backward fractional derivativesGeneralised Cauchy derivativeLiouville derivativeDifferintegrationCentral fractional derivativesFractional stochastic processFractional Brownian motionjournal article