The generalized solution of fractional di§erential equations sample with Brownian motion

It is well known that the solution of fractional models proved to be a powerful tool in studying various problems which appear in the sciences of real life. In view of the fact that economic applications are accelerating at an amazing pace, and the large number of modeling in this speciality, it has expanded the number of problems. So, our contribution is based on finding generalized solutions of a fractional differential equation known for their applications in microeconomics and finance and creating an algorithm which allows us to estimate the coefficients of this type of equation. And to really illustrate our results we will choose a model known in the stochastic literature by COGARCH but with fractional derivative, to demonstrate the asymptotic behavior of the estimators, including the impact of fractional order on the space of stochastic differential equations.