K. Shibata, A. Takahashi, and T. Shirai, Fault diagnosis of rotating machinery through visualisation of sound signals, Mechanical Systems and Signal Processing, vol.14, issue.2, pp.229-241, 2000.

A. Chaigne and J. Kergomard, Acoustics of Musical Instruments, vol.844, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01338980

E. L. Allgower and K. Georg, Introduction to Numerical Continuation Methods, Society for Industrial and Applied Mathematics, 2003.

B. Cochelin and C. , Vergez: A high order purely frequency-based harmonic balance formulation for continuation of periodic solutions, Journal of Sound and Vibration, vol.324, pp.243-262, 2009.

J. H. Smith and J. Woodhouse, The tribology of rosin, Journal of the Mechanics and Physics of Solids, vol.48, issue.8, pp.1633-1681, 2000.

P. Vigué, Solutions périodiques et quasi-périodiques de systèmes dynamiques d'ordre entier ou fractionnaire-Applications à la corde frottée, 2017.

H. Berjamin, B. Lombard, C. Vergez, and E. , Cottanceau: Time-domain numerical modeling of brass instruments including nonlinear wave propagation, viscothermal losses, and lips vibration, Acta Acustica united with Acustica, vol.103, issue.1, pp.117-131, 2017.

B. Lombard and D. Matignon, Diffusive approximation of a time-fractional Burger's equation in nonlinear acoustics, SIAM Journal on Applied Mathematics, vol.76, issue.5, pp.1765-1791, 2016.

O. Richoux, B. Lombard, and J. F. Mercier, Generation of acoustic solitary waves in a lattice of Helmholtz resonators, Wave Motion, vol.56, pp.85-99, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01069252

R. L. Bagley and P. J. Torvik, A theoretical basis for the application of fractional calculus to viscoelasticity, Journal of Rheology, vol.27, issue.3, pp.201-210, 1983.

R. Metzler, E. Barkai, and J. Klafter, Anomalous diffusion and relaxation close to thermal equilibrium: A fractional Fokker-Planck equation approach, Physical Review Letters, vol.82, issue.18, pp.3563-3567, 1999.

D. A. Benson, S. W. Wheatcraft, and M. M. Meerschaert, Application of a fractional advection-dispersion equation, Water Resources Research, vol.36, issue.6, pp.1403-1412, 2000.

Y. A. Rossikhin and M. V. Shitikova, Application of fractional calculus for dynamic problems of solid mechanics: novel trends and recent results, Applied Mechanics Reviews, vol.63, issue.1, pp.10801-10802, 2010.

R. Hilfer, Applications of Fractional Calculus in Physics, 2000.

C. Y. Zhang, Pseudo almost periodic solutions of some differential equations, Journal of Mathematical Analysis and Applications, vol.181, issue.1, pp.62-76, 1994.

R. Agarwal, B. De-andrade, and C. Cuevas, On type of periodicity and ergodicity to a class of fractional order differential equations, Advances in Difference Equations 1, pp.1-25, 2010.

R. Agarwal, C. Cuevas, H. Soto, and M. El-gebeily, Asymptotic periodicity for some evolution equations in Banach spaces, Nonlinear Analysis: Theory, Methods & Applications, vol.74, issue.5, pp.1769-1798, 2011.

C. Lizama and G. M. N'guérékata, Mild solutions for abstract fractional differential equations, Applicable Analysis, vol.92, issue.8, pp.1731-1754, 2013.

V. Mishra, S. Das, H. Jafari, and . Ong, Study of fractional order van der Pol equation, Journal of King Saud University-Science, vol.28, issue.1, pp.55-60, 2016.

M. Belmekki, J. Nieto, and R. Rodriguez-lopez, Existence of periodic solution for a nonlinear fractional differential equation. Boundary Value Problems 1, pp.1-18, 2009.

K. Diethelm, N. J. Ford, and A. D. , Freed: A predictor-corrector approach for the numerical solution of fractional differential equations, Nonlinear Dynamics, vol.29, issue.1, pp.3-22, 2002.

M. Aoun, R. Malti, F. Levron, and A. , Oustaloup: Numerical simulations of fractional systems: an overview of existing methods and improvements, Nonlinear Dynamics, vol.38, issue.1-4, pp.117-131, 2004.

P. Kumar and O. P. , Agrawal: An approximate method for numerical solution of fractional differential equations, Signal Processing, vol.86, issue.10, pp.2602-2610, 2006.

A. H. Bhrawy, T. M. Taha, and J. A. Machado, A review of operational matrices and spectral techniques for fractional calculus, Nonlinear Dynamics, vol.81, issue.3, pp.1023-1052, 2015.

R. Hilfer, Threefold Introduction to Fractional Derivatives. Anomalous Transport: Foundations and Applications, pp.17-73, 2008.

M. D. Ortigueira, Fractional Calculus for Scientists and Engineers, vol.84, 2011.

I. Podlubny, Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, vol.198, 1998.

I. Petrá?, Fractional-order nonlinear systems: modeling, analysis and simulation, 2011.

A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol.204, 2006.

K. Diethelm, An investigation of some nonclassical methods for the numerical approximation of Caputotype fractional derivatives, Numer. Algor, vol.47, pp.361-390, 2008.

S. Karkar, B. Cochelin, and C. , Vergez: A high-order, purely frequency based harmonic balance formulation for continuation of periodic solutions: The case of non-polynomial nonlinearities, Journal of Sound and Vibration, vol.332, issue.4, pp.968-977, 2013.

L. Guillot, P. Vigué, C. Vergez, and B. , Cochelin: Continuation of quasi-periodic solutions with two-frequency Harmonic Balance Method, Journal of Sound and Vibration, vol.394, pp.434-450, 2017.

E. Kaslik and S. Sivasundaram, Non-existence of periodic solutions in fractional-order dynamical systems and a remarkable difference between integer and fractional-order derivatives of periodic functions, Analysis: Real World Applications, vol.13, issue.3, pp.1489-1497, 2012.

J. Wang, M. Feckan, and Y. Zhou, Nonexistence of periodic solutions and asymptotically periodic solutions for fractional differential equations, Communications in Nonlinear Science and Numerical Simulation, vol.18, issue.2, pp.246-256, 2013.

I. Area, J. Losada, and J. J. Nieto, On fractional derivatives and primitives of periodic functions, Abstract and Applied Analysis, 2014.

C. M. Pinto and J. A. Machado, Complex-order forced Van der Pol oscillator, Journal of Vibration and Control, vol.18, issue.14, pp.2201-2209, 2012.

M. S. Tavazoei, M. Haeri, M. Attari, S. Bolouki, and M. Siami, More details on analysis of fractional-order van der Pol oscillator, Journal of Vibration and Control, vol.15, issue.6, pp.803-819, 2009.

J. H. Chen and W. C. Chen, Chaotic dynamics of the fractionally damped van der Pol equation, Chaos, Solitons & Fractals, vol.35, issue.1, pp.188-198, 2008.

T. Sardar, S. S. Ray, R. K. Bera, and B. B. , Biswas: The analytical approximate solution of the multi-term fractionally damped van der Pol equation, Physica Scripta, vol.80, issue.2, p.25003

A. Lazarus and O. Thomas, A harmonic-based method for computing the stability of periodic solutions of dynamical systems, Comptes Rendus Mecanique, vol.338, issue.9, pp.510-517, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01452004

D. Matignon, Stability results for fractional differential equations with applications to control processing. Computational engineering in systems applications, vol.2, pp.963-968, 1996.

E. Kaslik and S. , Sivasundaram: Nonlinear dynamics and chaos in fractional-order neural networks, Neural Networks, vol.32, pp.245-256, 2012.

E. Cuesta, Asymptotic behaviour of the solutions of fractional integro-differential equations and some time discretizations. Discrete and Continuous Dynamical Systems, Supplement, pp.277-285, 2007.