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

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