Fractional Calculus: Theory and Applications

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...

Analytic function theory, fractional calculus and their 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...

Calculus, Applications and Theory

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...