Fractional calculus and its applications

Fractional calculus and its applications.

Fractional calculus was formulated in 1695, shortly after the development of classical calculus. The earliest systematic studies were attributed to Liouville, Riemann, Leibniz, etc. [1,2]. For a long time, fractional calculus has been regarded as a pure mathematical realm without real applications. But, in recent decades, such a state of affairs has been changed. It has been found that fraction...

Fractional Brownian motion: stochastic calculus and applications

Fractional Brownian motion (fBm) is a centered self-similar Gaussian process with stationary increments, which depends on a parameter H ∈ (0, 1) called the Hurst index. In this note we will survey some facts about the stochastic calculus with respect to fBm using a pathwise approach and the techniques of the Malliavin calculus. Some applications in turbulence and finance will be discussed. Math...

Theory, Methods, and Applications of Fractional Calculus

1 Institute for Groundwater Studies, University of the Free State, Bloemfontein 9300, South Africa 2Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia 3 Department of Mathematical Sciences, North-West University, Mafikeng Campus, Mmabatho 2735, South Africa 4Department of Mathematical Engineering, Yildiz Technical Univ...

Some Applications of Fractional Calculus in Engineering

Fractional Calculus FC goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a prelimina...

Malliavin calculus and its applications