Ortigueira, M.
2006.
A coherent approach to non-integer order derivatives. Signal Processing. 86:2505–2515., Number 10: Elsevier
AbstractThe relation showing that the Grunwald-Letnikov and generalised Cauchy derivatives are equal is presented. This establishes a bridge between two different formulations and simultaneously between the classic integer order derivatives and the fractional ones. Starting from the generalised Cauchy derivative formula, new relations are obtained, namely a regularised version that makes the concept of pseudo-function appear naturally without the need for a rejection of any infinite part. From the regularised derivative, new formulations are deduced and specialised first for the real functions and afterwards for functions with Laplace transforms obtaining the definitions proposed by Lionville. With these tools suitable definitions of fractional linear systems are obtained.
Ortigueira, M.
2009.
Comments on ?Modeling fractional stochastic systems as non-random fractional dynamics driven Brownian motions? Applied Mathematical Modelling. 33:2534–2537., Number 5: Elsevier Inc.
AbstractSome results presented in the paper ?Modeling fractional stochastic systems as non-random fractional dynamics driven Brownian motions? ?I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999? are discussed in this paper. The slightly modified Grünwald-Letnikov derivative proposed there is used to deduce some interesting results that are in contradiction with those proposed in the referred paper.
Ortigueira, MD.
2009.
Comments on ?Modeling fractional stochastic systems as non-random fractional dynamics driven Brownian motions? Applied Mathematical Modelling. 33:2534–2537., Number 5
AbstractSome results presented in the paper ?Modeling fractional stochastic systems as non-random fractional dynamics driven Brownian motions? ?I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999? are discussed in this paper. The slightly modified Grünwald-Letnikov derivative proposed there is used to deduce some interesting results that are in contradiction with those proposed in the referred paper. Keywords: Fractional calculus; Grünwald-Letnikov derivative; Fractional Brownian motion
Xanthopoulos, P, Golemati S, Sakkalis V, Ktonas PY, Ortigueira M, Zervakis M, Paparrigopoulos T, Tsekou H, Soldatos CR.
2006.
Comparative analysis of time-frequency methods estimating the time-varying microstructure of sleep EEG spindles, October. Information Technology Applications in Biomedicine.
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