On the Construction of a New Fractional Brownian Motion - Mahmoud M. El-Borai; Khairia El-Said El-Nadi (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.