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, Proc. 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

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

B. Guo, J. Li, and H. Zmuda, A New FDTD Formulation for Wave Propagation in Biological Media With Cole–Cole Model, IEEE Microwave and Wireless Components Letters, vol.16, issue.12, pp.633-635, 2006.
DOI : 10.1109/LMWC.2006.885583

J. Bai and X. C. Feng, Fractional-Order Anisotropic Diffusion for Image Denoising, IEEE Transactions on Image Processing, vol.16, issue.10, pp.2492-2502, 2007.
DOI : 10.1109/TIP.2007.904971

A. Savitzky and M. J. Golay, Smoothing and Differentiation of Data by Simplified Least Squares Procedures., Analytical Chemistry, vol.36, issue.8, pp.1627-1639, 1964.
DOI : 10.1021/ac60214a047

R. W. Schafer, What Is a Savitzky-Golay Filter? [Lecture Notes], IEEE Signal Processing Magazine, vol.28, issue.4, pp.111-117, 2011.
DOI : 10.1109/MSP.2011.941097

P. O. Persson and G. Strang, Smoothing by Savitzky-Golay and Legendre filters, IMA Volume on Math, Systems Theory in Biology Comm., Comp., and Finance, vol.134, pp.301-316, 2003.

P. Meer and I. Weiss, Smoothed differentiation filters for images, Journal of Visual Communication and Image Representation, vol.3, issue.1, pp.58-72, 1992.
DOI : 10.1016/1047-3203(92)90030-W

P. Craven and G. Wahba, Smoothing noisy data with spline functions, Numerische Mathematik, vol.4, issue.4, pp.377-403, 1979.
DOI : 10.1007/BF01404567

S. Ibrir and S. Diop, A numerical procedure for filtering and efficient high-order signal differentiation, Internat. J. Appl. Math. Comput. Sci, vol.14, pp.201-208, 2004.

D. L. Chen, Y. Q. Chen, and D. Y. Xue, 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

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, 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, LNCS, vol.6920, pp.45-55, 2011.

D. Y. Liu, O. Gibaru, W. Perruquetti, and T. M. Laleg-kirati, Fractional order differentiation by integration with Jacobi polynomials, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), 2012.
DOI : 10.1109/CDC.2012.6426436

URL : https://hal.archives-ouvertes.fr/hal-00728406

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

M. Fliess, C. Join, M. Mboup, and H. Sira-ramrez, 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

M. Fliess and H. Sira-ramrez, An algebraic framework for linear identification, ESAIM Control Optim, Analyse non standard du bruit, Comptes Rendus Mathematique, pp.151-168, 2003.

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

D. N. Hao, L. H. Chuong, and L. Desnic, Heuristic regularization methods for numerical differentiation, Computers & Mathematics with Applications, vol.63, issue.4, pp.816-826, 2012.
DOI : 10.1016/j.camwa.2011.11.047

X. Li, Numerical solution of fractional differential equations using cubic B-spline wavelet collocation method, Communications in Nonlinear Science and Numerical Simulation, vol.17, issue.10, pp.3934-3946, 2012.
DOI : 10.1016/j.cnsns.2012.02.009

P. Massopust, Interpolation and Approximation with Splines and Fractals, 2010.

C. De-boor, A Practical Guide to Splines, 1978.
DOI : 10.1007/978-1-4612-6333-3

J. Hadamard, Sur lesprobì emes aux dérivées partielles et leur signification physique, pp.49-52, 1902.

S. Diop, J. W. Grizzle, and F. Chaplais, On numerical differentiation algorithms for nonlinear estimation, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187), 2000.
DOI : 10.1109/CDC.2000.912005

A. N. Tikhonov and V. Y. Arsenin, Solution of Illposed Problems, 1977.

P. C. Hansen, REGULARIZATION TOOLS: A Matlab package for analysis and solution of discrete ill-posed problems, Numerical Algorithms, vol.55, issue.Suppl., 2008.
DOI : 10.1007/BF02149761

S. Haykin and B. Van-veen, Signals and Systems, 2002.

K. S. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, 1993.