[1] N. H. Sweilam and T. M. Al-Ajami, Legendre spectral-collocation method for solving some
types of fractional optimal control problems, Journal of Advanced Research, vol. 6 (2015),
pp. 393-403.

[2] A. Lotfi, M. Dehghan and S. A. Yousefi, A numerical technique for solving fractional optimal
control problems, Computer and mathematics with applications, vol. 62 (2011), pp. 1055-1067.

[3] T. L. Guo, The necessary conditions of fractional optimal control in the sense of caputo, J.
Optim Theory Appl, vol. 156 (2013), pp. 115-126.

[4] O. P. Agrawal, A formulation and numerical schem for fractional optimal control problems, J.
Vib. control, vol. 13 (2007), pp. 1291-1299.
[Web of Science]

[5] A. Lotfi and S. Yousefi, A numerical technique for solving a class of fractional variational
problems, J. Comput. Appl. Math., vol. 237 (2013), pp. 633-643.

[6] A. Lotfi, S. Yousefi and M. Dehghan, Numerical solution of a class of fractional optimal control
problems via the legendre orthonormal basis combined with the operational matrix and the gauss
quadrature rule, Journal of Computational and Applied Mathematics, vol. 250 (2013), pp. 143-
160.
[Web of Science]

[7] O. M. P. Agrawal, M. M. Hasan and X. W. Tangpong, A numerical scheme for a class of
parametric problem of fractional variational calculus, J. Comput. Nonlinear Dyn., vol. 7 (2012),
pp. 021005-021011.
[Web of Science]

[8] R. Almedia and D. F. M. Torres, Necessary and sufficient conditions for the fractional calculus
of variations with caputo derivatives, Commun. Nonlinear Sci. Numer. Simul, vol. 16 (2011),
pp. 1490-1500.
[Web of Science] [Crossref]

[9] R. Almedia and D. F. M. Torres, Calculus of variations with fractional derivatives and frac-
tional integrals, Appl. Math. Lett, vol. 22 (2009), pp. 1816-1820.
[Web of Science]

[10] O. M. P. Agrawal, A general finite element formulation for fractional variational problems, J.
Math. Anal. Appl., vol. 337 (2008), pp. 1-12.

[11] S. Djennounea and M. Bettaye, Optimal synergetic control for fractional-order systems, Auto-
matica, vol. 49 (2013), p. 2243.

[12] R. Toledo-Hernandez, V. Rico-Ramirez, R. Rico-Martinez, S. Hernandez-Castro and U. M.
Diwekar, A fractional calculus approach to the dynamic optimization of biological reactive sys-
tems. part ii: Numerical solution of fractional optimal control problems, Chemical Engineering
Science, vol. 117 (2014), pp. 239-247.
[Web of Science]

[13] R. Kamocki, On the existence of optimal solutions to fractional optimal control problems,
Applied Mathematics and Computation, vol. 235 (2014), pp. 94-104.

[14] G. M. Mophoua and G. M. Niguerekata, Optimal control of a fractional diffusion equation with
state constraints, Computers and Mathematics with Applications, vol. 62 (2011), pp. 1413-
1426.

[15] M. Abedini, M. A. Nojoumian, H. Salarieh and A. Meghdari, Model reference adaptive control
in fractional order systems using discrete-time approximation methods, Commun Nonlinear
Sci Numer Simulat, vol. 25 (2015), pp. 27-40.
[Web of Science] [Crossref]

[16] Z. D. Jelicic and N. Petrovacki, Optimality conditions and a solution scheme for fractional
optimal control problems, Struct Multidisc Optim, vol. 38 (2009), pp. 571-581.

[17] A. Lotfi and S. A. Yousefi, Epsilon-ritz method for solving a class of fractional constrained
optimization problems, J. Optim Theory Appl, vol. 163 (2014), pp. 884-899.

[18] F. Jarad, T. Abdeljawad and D. Baleanu, Fractional variational optimal control problems with
delayed arguments, m Nonlinear Dyn, vol. 62 (2010), pp. 609-614.

[19] A. H. Bhrawy, E. H. Doha, J. A. T. Machado and S. Ezz-Eldien, An efficient numerical scheme
for solving multi-dimensional fractional optimal control problems with a quadratic performance
index, Asian Journal of Control, DOI: 10.1002/asjc.1109, 2015.
[Crossref] [Web of Science]

[20] A. Bhrawy, T. Taha and J. A. T. Machado, A review of operational matrices and spectral
techniques for fractional calculus, Nonlinear Dynamics, vol. 81 (2015), pp. 1023-1052.
[Web of Science]

[21] S. Ezz-Eldien, E. Doha, D. Baleanu and A. Bhrawy, A numerical approach based on Legendre
orthonormal polynomials for numerical solutions of fractional optimal control problems, Journal
of Vibration and Control, DOI: 10.1177/1077546315573916, 2015.
[Web of Science] [Crossref]

[22] A. Bhrawy, E. Doha, D. Baleanu, S. Ezz-Eldien and M. Abdelkawy, An accurate numerical
technique for solving fractional optimal control problems, Proc. Rom. Acad. A, vol. 16(1)
(2015), pp. 47-54.

[23] I. Podlubny, Fractional Differential Equations. San Diego: Academic Press, 1999.

[24] M. P. Tripathi, V. K. Baranwal, R. K. Pandey and O. P. Singh, A new numerical algorithm to
solve fractional differential equations based on operational matrix of generalized hat functions,
Commun Nonlinear Sci Numer Simulat, vol. 18 (2013), pp. 1327-1340.
[Web of Science] [Crossref]

[25] M. H. Heydari, M. R. Hooshmandasl, F. M. M. Ghaini and C. Cattani, A computational method
for solving stochastic it^o-volterra integral equations based on stochastic operational matrix for
generalized hat basis functions, J. Comput. Phys., vol. 270 (2014), pp. 402-415.
[Web of Science]

[26] M. H. Heydari, M. R. Hooshmandasl, C. Cattani and F. M. M. Ghaini, An efficient computa-
tional method for solving nonlinear stochastic it^o integral equations: Application for stochastic
problems in physics, J. Comput. Phys., vol. 283 (2015), pp. 148-168.
[Web of Science]

[27] E. Babolian and M. Mordad, A numerical method for solving systems of linear and nonlinear
integral equations of the second kind by hat basis function, Comput. Math. Appl., vol. 62
(2011), pp. 187-198.

[28] S. Momani and Z. Odibat, Numerical approach to differential equations of fractional order, J.
Comput. Appl. Math, vol. 207 (2007), pp. 96-110.

Published Online: 2016-02-26Citation Information:Tbilisi Mathematical Journal. Volume 9, Issue 1, Pages 143–157, ISSN (Online) 1512-0139, DOI: https://doi.org/10.1515/tmj-2016-0007, February 2016© 2016 . This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. (CC BY-NC-ND 3.0)