Ortigueira, MD, Batista AG.
2004.
A Fractional Linear System View of the Fractional Brownian Motion, December. Nonlinear Dynamics. 38:295–303., Number 1-4: Springer
AbstractA definition of the fractional Brownian motion based on the fractional differintegrator characteristics is proposed and studied. It is shown that the model enjoys the usually required properties. A discrete-time version based in the backward difference and in the bilinear transformation is considered. Some results are presented.
Ortigueira, MD.
2010.
The fractional quantum derivative and its integral representations? Communications in Nonlinear Science and Numerical Simulation. 15:956–962., Number 4: Elsevier B.V.
AbstractThe quantum fractional derivative is defined using formulations analogue to the common Grünwald?Letnikov derivatives. While these use a linear variable scale, the quantum derivative uses an exponential scale and is defined in R? or R?. Two integral formulations similar to the usual Liouville derivatives are deduced with the help of the Mellin transform.
Ortigueira, MD, Coito F.
2004.
From Differences to Derivatives. Fractional Calculus and Applied Analysis. 7:459., Number 4: INSTITUTE OF MATHEMATICS AND INFORMATICS BULGARIAN ACADEMY OF SCIENCES
Abstract
Ortigueira, MD, Trujillo JJ.
2011.
Generalized Gru?nwald?Letnikov Fractional Derivative and Its Laplace and Fourier Transforms Journal of Computational and Nonlinear Dynamics. 6:034501., Number 3
AbstractThe generalized Grünwald?Letnikov fractional derivative is analyzed in this paper. Its Laplace and Fourier transforms are computed, and some current results are criticized. It is shown that only the forward derivative of a sinusoid exists. This result is used to define the frequency response of a fractional linear system.
Valério, D, Ortigueira MD, da Costa JSá.
2008.
Identifying a Transfer Function From a Frequency Response, April. Journal of Computational and Nonlinear Dynamics. 3:021207., Number 2
AbstractIn this paper, the classic Levy identification method is reviewed and reformulated using a complex representation. This new formulation addresses the well known bias of the classic method at low frequencies. The formulation is generic, coping with both integer order and fractional order transfer functions. A new algorithm based on a stacked matrix and its pseudoinverse is proposed to accommodate the data over a wide range of frequencies. Several simulation results are presented, together with a real system identification. This system is the Archimedes Wave Swing, a prototype of a device to convert the energy of sea waves into electricity.
Ortigueira, MD.
2008.
An introduction to the fractional continuous-time linear systems: the 21st century systems. IEEE Circuits and Systems Magazine. 8:19–26., Number 3: IEEE
AbstractA 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.
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