On the Construction of a New Fractional Brownian Motion - El-Borai, Mahmoud M.; El-Nadi, Khairia El-Said (Mathematics and Computer Science: Contemporary Developments Vol. 9, 2024)
A fractional normal distribution is constructed. With the help of this new distribution, a fractional Brownian motion is defined. A generalization of the Ito stochastic integration is given and some stochastic properties are studied. Formula Ito and the product rule are generalized.