Introduction to fractional linear systems. Part 2: discrete-time case

IEE Proceedings - Vision, Image, and Signal Processing, Vol. 147, nº 1

An introduction to the fractional continuous-time linear systems

A brief introduction to the fractional continuous-time linear systems is presented. It will be done without needing a deep study of the fractional derivatives. We will show that the computation of the impulse and step responses is very similar to the classic. The main difference lies in the substitution of the exponential by the Mittag-Leffler function. We will present also the main formulae defining the fractional derivatives.

On the fractional central differences and derivatives

Fractional central differences and derivatives are studied in this article. These are generalisations to real orders of the ordinary positive (even and odd) integer order differences and derivatives, and also coincide with the well known Riesz potentials. The coherence of these definitions is studied by applying the definitions to functions with Fourier transformable functions. Some properties of these derivatives are presented and particular cases studied.

An introduction to the fractional continuous- time linear systems: the 21st century systems

IEEE CIRCUITS AND SYSTEMS MAGAZINE, Third Quarter

Fractional central differences and derivatives

Journal of Vibration and Control, Vol. 14, Nº 9-10

On the relation between the fractional Brownian motion and the fractional derivatives

Physics Letters A, vol. 372; Issue 7

Pseudo-fractional ARMA modelling using a double Levinson recursion

IET Control Theory & Applications, Vol. 1, Nº 1

A fractional linear system view of the fractional brownian motion

Nonlinear Dynamics, Vol. 38

Fractional central differences and derivatives

Journal of Vibration and Control, 14(9–10): 1255–1266, 2008

Comments on ‘‘Modeling fractional stochastic systems as non-random fractional dynamics driven Brownian motions

Applied Mathematical Modelling, Vol.33

A new least-squares approach to differintegration modeling

Signal Processing, Vol. 86, nº 10

Riesz potential operators and inverses via fractional centred derivatives

International Journal of Mathematics and Mathematical Sciences, Vol.2006

A new symmetric fractional B-spline

Signal Processing, Vol. 83, nº 11

On the initial conditions in continuous-time fractional linear systems

Signal Processing, Vol. 83, nº 11

Fractional discrete-time signal processing: scale conversion and linear prediction

Nonlinear Dynamics, Vol. 29