On the solution of the stochastic differential equation of exponential growth driven by fractional Brownian motion

It is shown that, by using Taylor's series of fractional order, the stochastic differential equation dx=σxdb(t,a), where b(t,a) is a fractional Brownian motion of order a, can be converted into an equation involving fractional derivative, therefore a solution expressed in terms of the Mittag-Leffler function.