We consider the functions 1/f and h/f , and study some properties of the successive derivatives of these functions. We also study certain integer sequences connected with these successive derivatives.

Classical and anomalous diffusion equations employ integer derivatives, fractional derivatives, and other pseudodifferential operators in space. In this paper we show that replacing the integer time derivative by a fractional derivative subordinates the original stochastic solution to an inverse stable subordinator process whose probability distributions are Mittag-Leffler type. This leads to e...

Discrete-time fractional derivative filters (1-D and 2-D) are shown to be well approximated from a small set of integer derivatives. A fractional derivative of arbitrary order (and, in 2-D, of arbitrary orientation) can therefore be efficiently computed from a linear combination of integer derivatives of the underlying signal or image.

A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of various types of fractional diffusion equation. The suggested method is the development of Podlubny’s matrix approach (Fractional Calculus and Applied Analysis, ...