D. L. Chen, Y. Q. Chen, and D. Y. , Digital Fractional Order Savitzky-Golay Differentiator, IEEE Transactions on Circuits and Systems II: Express Briefs, vol.58, issue.11, pp.758-762, 2011.
DOI : 10.1109/TCSII.2011.2168022
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.648.5648

M. Cugnet, J. Sabatier, S. Laruelle, S. Grugeon, B. Sahut et al., On Lead-Acid-Battery Resistance and Cranking-Capability Estimation, IEEE Transactions on Industrial Electronics, vol.57, issue.3, pp.909-917, 2010.
DOI : 10.1109/TIE.2009.2036643
URL : https://hal.archives-ouvertes.fr/hal-00413746

M. Fliess and R. Hotzel, Sur les systèmes linéaireslinéaires`linéairesà dérivation non entì ere, C.R. Acad. Sci. Paris Ser. IIb, vol.324, pp.99-105, 1997.

M. Fliess, Analyse non standard du bruit, Comptes Rendus Mathematique, vol.342, issue.10, pp.797-802, 2006.
DOI : 10.1016/j.crma.2006.02.037
URL : https://hal.archives-ouvertes.fr/inria-00001134

M. Fliess, Critique du rapport signaì a bruit en communications numériques ? Questioning the signal to noise ratio in digital communications, International Conference in Honor of Claude Lobry, Revue africaine d'informatique et de Mathématiques appliquées, pp.419-429, 2008.

M. Fliess and H. Sira-ramírez, An algebraic framework for linear identification, ESAIM: Control, Optimisation and Calculus of Variations, vol.9, pp.151-168, 2003.
DOI : 10.1051/cocv:2003008

M. Fliess and H. Sira-ramírez, Closed-loop Parametric Identification for Continuous-time Linear Systems via New Algebraic Techniques
DOI : 10.1007/978-1-84800-161-9_13
URL : https://hal.archives-ouvertes.fr/inria-00114958

M. Fliess, M. Mboup, H. Mounier, and H. Sira-ramírez, Questioning some paradigms of signal processing via concrete examples, Algebraic Methods in Flatness, Signal Processing and State Estimation Editiorial Lagares, pp.1-21, 2003.
URL : https://hal.archives-ouvertes.fr/inria-00001059

M. Fliess, C. Join, M. Mboup, and H. Sira-ramírez, Compression diff??rentielle de transitoires bruit??s, Comptes Rendus Mathematique, vol.339, issue.11, pp.821-826, 2004.
DOI : 10.1016/j.crma.2004.10.003

R. Hotzel and M. Fliess, On linear systems with a fractional derivation: Introductory theory and examples, Mathematics and Computers in Simulation, vol.45, issue.3-4, pp.385-395, 1998.
DOI : 10.1016/S0378-4754(97)00118-3

G. Jumarie, Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results, Computers & Mathematics with Applications, vol.51, issue.9-10, pp.1367-1376, 2006.
DOI : 10.1016/j.camwa.2006.02.001

G. Jumarie, Table of some basic fractional calculus formulae derived from a modified Riemann???Liouville derivative for non-differentiable functions, Applied Mathematics Letters, vol.22, issue.3, pp.378-385, 2009.
DOI : 10.1016/j.aml.2008.06.003

G. Jumarie, Fourier's transform of fractional order via Mittag-Leffler function and modified Riemann-Liouville derivative, J. Appl. Math. Inform, vol.26, pp.1101-1121, 2008.

G. Jumarie, Laplace???s transform of fractional order via the Mittag???Leffler function and modified Riemann???Liouville derivative, Applied Mathematics Letters, vol.22, issue.11, pp.1659-1664, 2009.
DOI : 10.1016/j.aml.2009.05.011

D. Y. Liu, O. Gibaru, W. Perruquetti, M. Fliess, and M. Mboup, An error analysis in the algebraic estimation of a noisy sinusoidal signal, 2008 16th Mediterranean Conference on Control and Automation, 2008.
DOI : 10.1109/MED.2008.4602161
URL : https://hal.archives-ouvertes.fr/inria-00300234

D. Y. Liu, O. Gibaru, and W. Perruquetti, Parameters estimation of a noisy sinusoidal signal with time-varying amplitude, 2011 19th Mediterranean Conference on Control & Automation (MED), 2009.
DOI : 10.1109/MED.2011.5983186
URL : https://hal.archives-ouvertes.fr/inria-00593408

D. Y. Liu, O. Gibaru, and W. Perruquetti, Differentiation by integration with Jacobi polynomials, Journal of Computational and Applied Mathematics, vol.235, issue.9, pp.3015-3032, 2011.
DOI : 10.1016/j.cam.2010.12.023
URL : https://hal.archives-ouvertes.fr/inria-00550160

D. Y. Liu, O. Gibaru, and W. Perruquetti, Error analysis of Jacobi derivative estimators for noisy signals, Numerical Algorithms, vol.21, issue.12, pp.53-83, 2011.
DOI : 10.1007/s11075-011-9447-8
URL : https://hal.archives-ouvertes.fr/inria-00573270

D. Y. Liu, O. Gibaru, and W. Perruquetti, Convergence Rate of the Causal Jacobi Derivative Estimator, Curves and Surfaces 2011, pp.45-55, 2011.
DOI : 10.1007/978-3-642-27413-8_28
URL : https://hal.archives-ouvertes.fr/inria-00599767

A. Loverro, Fractional calculus, history, definitions and applications for the engineer, 2004.

J. A. Machado, Calculation of fractional derivatives of noisy data with genetic algorithms, Nonlinear Dyn, pp.253-260, 2009.

M. Mboup, Parameter estimation for signals described by differential equations, Applicable Analysis, vol.26, issue.1, pp.29-52, 2009.
DOI : 10.1109/MED.2008.4602161

M. Mboup and C. , Join and M. Fliess: A revised look at numerical differentiation with an application to nonlinear feedback control, 15th Mediterranean conference on Control and automation (MED'07)

M. Mboup and C. , Join and M. Fliess: Numerical differentiation with annihilators in noisy environment, Numerical Algorithms 50, pp.439-467, 2009.

K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, 1933.

A. Neves, M. Mboup, and M. Fliess, An algebraic receiver for full response CPM demodulation, 2006 International Telecommunications Symposium, 2006.
DOI : 10.1109/ITS.2006.4433304
URL : https://hal.archives-ouvertes.fr/inria-00086115

A. Neves, M. D. Miranda, and M. Mboup, Algebraic parameter estimation of damped exponentials, Proc. 15 th Europ. Signal Processing Conf. - EUSIPCO 2007, 2007.
URL : https://hal.archives-ouvertes.fr/inria-00179732

K. B. Oldham and J. Spanier, The Fractional Calculus, 1974.

A. Oustaloup, B. Mathieu, and P. Lanusse, The CRONE Control of Resonant Plants: Application to a Flexible Transmission, European Journal of Control, vol.1, issue.2, pp.113-121, 1995.
DOI : 10.1016/S0947-3580(95)70014-0
URL : https://hal.archives-ouvertes.fr/hal-00182807

A. Oustaloup, J. Sabatier, and X. Moreau, From fractal robustness to the CRONE approach, ESAIM: Proceedings, pp.177-192, 1998.
DOI : 10.1051/proc:1998006
URL : https://hal.archives-ouvertes.fr/hal-00184273

A. Oustaloup, J. Sabatier, and P. Lanusse, From fractal robustness to the CRONE control, pp.1-30, 1999.
URL : https://hal.archives-ouvertes.fr/hal-00184272

V. Pommier, J. Sabatier, P. Lanusse, and A. Oustaloup, Crone control of a nonlinear hydraulic actuator, Control Engineering Practice, vol.10, issue.4, pp.391-402, 2002.
DOI : 10.1016/S0967-0661(01)00154-X
URL : https://hal.archives-ouvertes.fr/hal-00184274

S. Riachy, M. Mboup, and J. P. Richard, Multivariate numerical differentiation, Journal of Computational and Applied Mathematics, vol.236, issue.6, pp.1069-1089, 2011.
DOI : 10.1016/j.cam.2011.07.031
URL : https://hal.archives-ouvertes.fr/inria-00637164

S. Riachy, Y. Bachalany, M. Mboup, and J. P. Richard, An algebraic method for multi-dimensional derivative estimation, 2008 16th Mediterranean Conference on Control and Automation, 2008.
DOI : 10.1109/MED.2008.4602167
URL : https://hal.archives-ouvertes.fr/inria-00275461

S. Riachy, Y. Bachalany, M. Mboup, and J. P. Richard, Différenciation numérique multivariable I: estimateurs algébriques et structure, ieme Confrence Internationale Francophone d'Automatique, 2010.

J. R. Trapero, H. Sira-ramírez, and V. F. Battle, An algebraic frequency estimator for a biased and noisy sinusoidal signal, Signal Processing, vol.87, issue.6, pp.1188-1201, 2007.
DOI : 10.1016/j.sigpro.2006.10.006

R. Ushirobira, W. Perruquetti, M. Mboup, and M. Fliess, Estimation algébrique des paramètres intrinsèques d'un signal sinuso¨?dalsinuso¨?dal biaisé en environnement bruité, XXIII e Colloque Gretsi, 2011.

G. C. Wu and E. W. , Fractional variational iteration method and its application, Physics Letters A, vol.374, issue.25, pp.2506-2509, 2010.
DOI : 10.1016/j.physleta.2010.04.034

Y. Tian, T. Floquet, and W. Perruquetti, Fast state estimation in linear time-varying systems: An algebraic approach, 2008 47th IEEE Conference on Decision and Control, 2008.
DOI : 10.1109/CDC.2008.4739289
URL : https://hal.archives-ouvertes.fr/inria-00320976