Efficient Multistep Methods for Tempered Fractional Calculus: Algorithms and Simulations

Tempered fractional calculus

Fractional derivatives and integrals are convolutions with a power law. Multiplying by an exponential factor leads to tempered fractional derivatives and integrals. Tempered fractional diffusion equations, where the usual second derivative in space is replaced by a tempered fractional derivative, govern the limits of random walk models with an exponentially tempered power law jump distribution....

Spectral Methods for Tempered Fractional Differential Equations

In this paper, we first introduce fractional integral spaces, which possess some features: (i) when 0 < α < 1, functions in these spaces are not required to be zero on the boundary; (ii)the tempered fractional operators are equivalent to the Riemann-Liouville operator in the sense of the norm. Spectral Galerkin and Petrov-Galerkin methods for tempered fractional advection problems and tempered ...

Tempered Fractional Stable Motion

Tempered fractional stable motion adds an exponential tempering to the power-law kernel in a linear fractional stable motion, or a shift to the power-law filter in a harmonizable fractional stable motion. Increments from a stationary time series that can exhibit semi-long-range dependence. This paper develops the basic theory of tempered fractional stable processes, including dependence structu...

Tempered fractional Brownian motion

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...