R. Almeida, S. Pooseh, and D. F. Torres, Fractional variational problems depending on indefinite integrals, Nonlinear Anal, pp.1009-1025, 2012.
DOI : 10.1016/j.na.2011.02.028

URL : http://arxiv.org/abs/1102.3360

R. Almeida and D. F. Torres, Leitmann???s direct method for fractional optimization problems, Applied Mathematics and Computation, vol.217, issue.3, pp.956-962, 2010.
DOI : 10.1016/j.amc.2010.03.085

T. M. Atanackovi´catanackovi´c, S. Konjik, and S. Pilipovi´cpilipovi´c, Variational problems with fractional derivatives: Euler???Lagrange equations, Journal of Physics A: Mathematical and Theoretical, vol.41, issue.9, p.95201, 2008.
DOI : 10.1088/1751-8113/41/9/095201

T. M. Atanackovi´catanackovi´c and B. Stankovic, An expansion formula for fractional derivatives and its application, Fract. Calc, Appl. Anal, vol.7, issue.3, pp.365-378, 2004.

T. M. Atanackovi´catanackovi´c and B. Stankovic, On a numerical scheme for solving differential equations of fractional order, Mechanics Research Communications, vol.35, issue.7, pp.429-438, 2008.
DOI : 10.1016/j.mechrescom.2008.05.003

D. Baleanu, O. Defterli, and O. P. , A Central Difference Numerical Scheme for Fractional Optimal Control Problems, Journal of Vibration and Control, vol.15, issue.4, pp.583-597, 2009.
DOI : 10.1177/1077546308088565

URL : http://arxiv.org/abs/0811.4368

P. L. Butzer, A. A. Kilbas, and J. J. Trujillo, Stirling Functions of the Second Kind in the Setting of Difference and Fractional Calculus, Numerical Functional Analysis and Optimization, vol.33, issue.7-8, pp.7-8, 2003.
DOI : 10.1016/0012-365X(95)00112-A

S. Das, Functional fractional calculus for system identification and controls, 2008.

K. Diethelm, The analysis of fractional differential equations, Lecture Notes in Mathematics, 2004.

K. Diethelm, N. J. Ford, and A. D. Freed, A predictor-corrector approach for the numerical solution of fractional differential equations, Nonlinear Dynam, vol.29, pp.1-4, 2002.

V. D. Djordjevic and T. M. Atanackovic, Similarity solutions to nonlinear heat conduction and Burgers/Korteweg???deVries fractional equations, Journal of Computational and Applied Mathematics, vol.222, issue.2, pp.701-714, 2008.
DOI : 10.1016/j.cam.2007.12.013

URL : http://doi.org/10.1016/j.cam.2007.12.013

L. Elsgolts, Differential equations and the calculus of variations, translated from the Russian by George Yankovsky, 1973.

N. J. Ford and J. A. Connolly, Comparison of numerical methods for fractional differential equations, Communications on Pure and Applied Analysis, vol.5, issue.2, pp.289-306, 2006.
DOI : 10.3934/cpaa.2006.5.289

Z. D. Jelicic and N. Petrovacki, Optimality conditions and a solution scheme for fractional optimal control problems, Structural and Multidisciplinary Optimization, vol.124, issue.3, pp.571-581, 2009.
DOI : 10.1007/s00158-008-0307-7

A. A. Kilbas, Hadamard-type fractional calculus, J. Korean Math. Soc, vol.38, issue.6, pp.1191-1204, 2001.
DOI : 10.1007/978-3-0348-8007-7_10

A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and applications of fractional differential equations, North?Holland Mathematics Studies, vol.204, 2006.

P. Kumar and O. P. , An approximate method for numerical solution of fractional differential equations, Signal Process, pp.2602-2610, 2006.

L. P. Lebedev and M. J. Cloud, The calculus of variations and functional analysis, World Sci. Publishing NJ, vol.12, 2003.
DOI : 10.1142/5374

A. B. Malinowska and D. F. Torres, Generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative, Computers & Mathematics with Applications, vol.59, issue.9, pp.3110-3116, 2010.
DOI : 10.1016/j.camwa.2010.02.032

M. M. Meerschaert and C. Tadjeran, Finite difference approximations for fractional advection???dispersion flow equations, Journal of Computational and Applied Mathematics, vol.172, issue.1, pp.65-77, 2004.
DOI : 10.1016/j.cam.2004.01.033

URL : http://doi.org/10.1016/j.cam.2004.01.033

T. Odzijewicz, A. B. Malinowska, and D. F. Torres, Fractional variational calculus with classical and combined Caputo derivatives, Nonlinear Anal, pp.1507-1515, 2012.
DOI : 10.1016/j.na.2011.01.010

URL : http://arxiv.org/abs/1101.2932

I. Podlubny, Fractional differential equations, Mathematics in Science and Engineering, vol.198, 1999.

L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The mathematical theory of optimal processes, Translated from the Russian by K. N. Trirogoff, 1962.

S. Pooseh, R. Almeida, and D. F. Torres, Expansion Formulas in Terms of Integer-Order Derivatives for the Hadamard Fractional Integral and Derivative, Numerical Functional Analysis and Optimization, vol.12, issue.8, pp.301-319, 2012.
DOI : 10.1080/01630563.2011.647197

URL : https://hal.archives-ouvertes.fr/hal-00724710

S. Pooseh, R. Almeida, and D. F. Torres, Approximation of fractional integrals by means of derivatives, Computers & Mathematics with Applications, vol.64, issue.10, pp.3090-3100, 2012.
DOI : 10.1016/j.camwa.2012.01.068

URL : https://hal.archives-ouvertes.fr/hal-00724720

S. Pooseh, R. Almeida, and D. F. Torres, Discrete direct methods in the fractional calculus of variations, Computers & Mathematics with Applications, vol.66, issue.5, pp.668-676, 2013.
DOI : 10.1016/j.camwa.2013.01.045

F. Riewe, Nonconservative Lagrangian and Hamiltonian mechanics, Physical Review E, vol.53, issue.2, pp.1890-1899, 1996.
DOI : 10.1103/PhysRevE.53.1890

F. Riewe, Mechanics with fractional derivatives, Physical Review E, vol.55, issue.3, pp.3581-3592, 1997.
DOI : 10.1103/PhysRevE.55.3581

S. G. Samko and A. A. , Kilbas and O. I. Marichev, Fractional integrals and derivatives, translated from the 1987 Russian original, 1993.

J. A. Machado, V. Kiryakova, and F. Mainardi, Recent history of fractional calculus, Communications in Nonlinear Science and Numerical Simulation, vol.16, issue.3, pp.1140-1153, 2011.
DOI : 10.1016/j.cnsns.2010.05.027

URL : http://hdl.handle.net/10400.22/4149

J. A. Machado, M. F. Silva, R. S. Barbosa, I. S. Jesus, C. M. Reis et al., Some applications of fractional calculus in engineering, Math. Probl. Eng., Art. ID, vol.639801, issue.34, p.pp, 2010.