D. Y. Liu, O. Gibaru, W. Perruquetti, and T. M. Laleg-kirati, Fractional Order Differentiation by Integration and Error Analysis in Noisy Environment, IEEE Transactions on Automatic Control, vol.60, issue.11
DOI : 10.1109/TAC.2015.2417852
URL : https://hal.archives-ouvertes.fr/hal-01134780

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

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

B. Mathieu, P. Melchior, A. Oustaloup, and C. , Ceyral, Fractional differentiation for edge detection, Signal Process, pp.2421-2432, 2003.

M. Benmalek and A. Charef, Digital fractional order operators for R-wave detection in electrocardiogram signal, IET Signal Processing, vol.3, issue.5, pp.381-391, 2009.
DOI : 10.1049/iet-spr.2008.0094

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, Parameters estimation of a noisy sinusoidal signal with time-varying amplitude, 2011 19th Mediterranean Conference on Control & Automation (MED), pp.570-575, 2011.
DOI : 10.1109/MED.2011.5983186
URL : https://hal.archives-ouvertes.fr/inria-00593408

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

D. Y. Liu, O. Gibaru, and W. Perruquetti, Error analysis for a class of numerical differentiator: application to state observation, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, pp.8238-8243, 2009.
DOI : 10.1109/CDC.2009.5400907
URL : https://hal.archives-ouvertes.fr/inria-00437129

M. Mboup, C. Join, and M. Fliess, Numerical differentiation with annihilators in noisy environment, Numerical Algorithms, vol.14, issue.12, pp.439-467, 2009.
DOI : 10.1007/s11075-008-9236-1
URL : https://hal.archives-ouvertes.fr/inria-00319240

M. Mboup, C. Join, and M. Fliess, A revised look at numerical differentiation with an application to nonlinear feedback control, 2007 Mediterranean Conference on Control & Automation, 2007.
DOI : 10.1109/MED.2007.4433728
URL : https://hal.archives-ouvertes.fr/inria-00142588

D. Y. Liu, O. Gibaru, and W. Perruquetti, Convergence Rate of the Causal Jacobi Derivative Estimator, Curves and Surfaces, LNCS, vol.6920, pp.45-55, 2011.

A. Saadatmandi and M. Dehghan, A new operational matrix for solving fractional-order differential equations, Computers & Mathematics with Applications, vol.59, issue.3, pp.1326-1336, 2010.
DOI : 10.1016/j.camwa.2009.07.006