Zou,
S.
,
Abdelkhalik,
O.
,
Robinett,
R.
,
Bacelli,
G.
, and
Wilson,
D.
, 2017, “
Optimal Control of Wave Energy Converters,” Renewable Energy,
103, pp. 217–225.

[CrossRef]
Kolar,
B.
,
Rams,
H.
, and
Schlacher,
K.
, 2017, “
Time-Optimal Flatness Based Control of a Gantry Crane,” Control Eng. Pract.,
60, pp. 18–27.

[CrossRef]
Donkers,
M.
,
Schijndel,
J. V.
,
Heemels,
W.
, and
Willems,
F.
, 2017, “
Optimal Control for Integrated Emission Management in Diesel Engines,” Control Eng. Pract.,
61, pp. 206–216.

[CrossRef]
Titouche,
S.
,
Spiteri,
P.
,
Messine,
F.
, and
Aidene,
M.
, 2015, “
Optimal Control of a Large Thermic Process,” J. Process Control,
25, pp. 50–58.

[CrossRef]
Rodrigues,
F.
,
Silva,
C. J.
,
Torres,
D. F. M.
, and
Maurer,
H.
, 2018, “
Optimal Control of a Delayed HIV Model,” Discrete Contin. Dyn. Syst. Ser. B,
23(1), pp. 443–458.

Kilbas,
A. A.
,
Srivastava,
H. M.
, and
Trujillo,
J. J.
, 2006, “
Theory and Applications of Fractional Differential Equations,” North-Holland Mathematics Studies, Vol.
204,
Elsevier Science B.V, Amsterdam, The Netherlands.

Podlubny,
I.
, 1999, “
Fractional Differential Equations,” Mathematics in Science and Engineering, Vol.
198,
Academic Press Inc., San Diego, CA.

Monje,
C. A.
,
Chen,
Y.
,
Vinagre,
B. M.
,
Xue,
D.
, and
Feliu,
V.
, 2010, “
Fractional-Order Systems and Controls,” Advances in Industrial Control,
Springer, London.

Sabatier,
J.
,
Oustaloup,
A.
,
Garcia Iturricha,
A.
, and
Lanusse,
P.
, 2002, “
CRONE Control: Principles and Extension to Time-Variant Plants With Asymptotically Constant Coefficients,” Nonlinear Dyn.,
29(1/4), pp. 363–385.

[CrossRef]
Ibrir,
S.
, and
Bettayeb,
M.
, 2015, “
New Sufficient Conditions for Observer-Based Control of Fractional-Order Uncertain Systems,” Autom. J. IFAC,
59, pp. 216–223.

[CrossRef]
Razminia,
A.
, and
Torres,
D. F. M.
, 2013, “
Control of a Novel Chaotic Fractional Order System Using a State Feedback Technique,” Mechatronics,
23(7), pp. 755–763.

[CrossRef]
Shukla,
M. K.
, and
Sharma,
B. B.
, 2017, “
Stabilization of a Class of Fractional Order Chaotic Systems Via Backstepping Approach,” Chaos Solitons Fractals,
98, pp. 56–62.

[CrossRef]
Razminia,
K.
,
Razminia,
A.
, and
Tenreiro Machado,
J. A.
, 2014, “
Analysis of Diffusion Process in Fractured Reservoirs Using Fractional Derivative Approach,” Commun. Nonlinear Sci. Numer. Simul.,
19(9), pp. 3161–3170.

[CrossRef]
Razminia,
K.
,
Razminia,
A.
, and
Baleanu,
D.
, 2015, “
Investigation of the Fractional Diffusion Equation Based on Generalized Integral Quadrature Technique,” Appl. Math. Model,
39(1), pp. 86–98.

[CrossRef]
Jahanshahi,
S.
, and
Torres,
D. F. M.
, 2017, “
A Simple Accurate Method for Solving Fractional Variational and Optimal Control Problems,” J. Optim. Theory Appl.,
174(1), pp. 156–175.

[CrossRef]
Dabiri,
A.
,
Moghaddam,
B. P.
, and
Tenreiro Machado,
J. A.
, 2018, “
Optimal Variable-Order Fractional PID Controllers for Dynamical Systems,” J. Comput. Appl. Math.,
339, pp. 40–48.

[CrossRef]
Baleanu,
D.
,
Jajarmi,
A.
,
Bonyah,
E.
, and
Hajipour,
M.
, 2018, “
New Aspects of Poor Nutrition in the Life Cycle Within the Fractional Calculus,” Adv. Difference Equ.,
2018(230), pp. 1--14.

Jajarmi,
A.
, and
Baleanu,
D.
, 2018, “
A New Fractional Analysis on the Interaction of HIV With CD4+ T-Cells,” Chaos Solitons Fractals,
113, pp. 221–229.

[CrossRef]
Kumar,
D.
,
Singh,
J.
, and
Baleanu,
D.
, 2018, “
Modified Kawahara Equation Within a Fractional Derivative With Non-Singular Kernel,” Therm. Sci.,
22(2), pp. 789–796.

[CrossRef]
Kumar,
D.
,
Singh,
J.
, and
Baleanu,
D.
, “
A New Fractional Model for Convective Straight Fins With Temperature-Dependent Thermal Conductivity,” Therm. Sci., (in Press).

Kumar,
D.
,
Singh,
J.
,
Baleanu,
D.
, and
Sushila
, 2018, “
Analysis of Regularized Long-Wave Equation Associated With a New Fractional Operator With Mittag-Leffler Type Kernel,” Phys. A,
492, pp. 155–167.

[CrossRef]
Kumar,
D.
,
Singh,
J.
, and
Baleanu,
D.
, 2018, “
A New Numerical Algorithm for Fractional Fitzhugh-Nagumo Equation Arising in Transmission of Nerve Impulses,” Nonlinear Dyn.,
91(1), pp. 307–317.

[CrossRef]
Kumar,
D.
,
Agarwal,
R. P.
, and
Singh,
J.
, 2018, “
A Modified Numerical Scheme and Convergence Analysis for Fractional Model of Lienard's Equation,” J. Comput. Appl. Math.,
339, pp. 405–413.

[CrossRef]
Ali,
H. M.
,
Lobo Pereira,
F.
, and
Gama,
S. M. A.
, 2016, “
A New Approach to the Pontryagin Maximum Principle for Nonlinear Fractional Optimal Control Problems,” Math. Methods Appl. Sci,
39(13), pp. 3640–3649.

[CrossRef]
Agrawal,
O. P.
, 2004, “
A General Formulation and Solution Scheme for Fractional Optimal Control Problems,” Nonlinear Dyn.,
38(1–4), pp. 323–337.

[CrossRef]
Almeida,
R.
, and
Torres,
D. F. M.
, 2009, “
Calculus of Variations With Fractional Derivatives and Fractional Integrals,” Appl. Math. Lett.,
22(12), pp. 1816–1820.

[CrossRef]
Debbouche,
A.
,
Nieto,
J. J.
, and
Torres,
D. F. M.
, 2017, “
Optimal Solutions to Relaxation in Multiple Control Problems of Sobolev Type With Nonlocal Nonlinear Fractional Differential Equations,” J. Optim. Theory Appl.,
174(1), pp. 7–31.

[CrossRef]
Razminia,
A.
,
Majd,
V. J.
, and
Feyz Dizaji,
A.
, 2012, “
An Extended Formulation of Calculus of Variations for Incommensurate Fractional Derivatives With Fractional Performance Index,” Nonlinear Dyn.,
69(3), pp. 1263–1284.

[CrossRef]
Odzijewicz,
T.
,
Malinowska,
A. B.
, and
Torres,
D. F. M.
, 2012, “
Generalized Fractional Calculus With Applications to the Calculus of Variations,” Comput. Math. Appl.,
64(10), pp. 3351–3366.

[CrossRef]
Razminia,
A.
,
Baleanu,
D.
, and
Majd,
V. J.
, 2013, “
Conditional Optimization Problems: Fractional Order Case,” J. Optim. Theory Appl.,
156(1), pp. 45–55.

[CrossRef]
Jajarmi,
A.
,
Hajipour,
M.
,
Mohammadzadeh,
E.
, and
Baleanu,
D.
, 2018, “
A New Approach for the Nonlinear Fractional Optimal Control Problems With External Persistent Disturbances,” J. Franklin Inst.,
355(9), pp. 3938–3967.

[CrossRef]
Zaky,
M. A.
, 2018, “
A Legendre Collocation Method for Distributed-Order Fractional Optimal Control Problems,” Nonlinear Dyn.,
91(4), pp. 2667–2681.

[CrossRef]
Dzielinski,
A.
, and
Czyronis,
P. M.
, 2014, “
Dynamic Programming for Fractional Discrete-Time Systems,” IFAC Proc. Vol.,
47(3), pp. 2003–2009.

[CrossRef]
Czyronis,
P. M.
, 2014, “
Dynamic Programming Problem for Fractional Discrete-Time Dynamic Systems. Quadratic Index of Performance Case,” Circuits Syst. Signal Process,
33(7), pp. 2131–2149.

[CrossRef]
Kolokoltsov,
V. N.
, and
Veretennikova,
M. A.
, 2014, “
A Fractional Hamilton Jacobi Bellman Equation for Scaled Limits of Controlled Continuous Time Random Walks,” Commun. Appl. Ind. Math.,
6(1), p. e–484.

Li,
C.
, and
Deng,
W.
, 2007, “
Remarks on Fractional Derivatives,” Appl. Math. Comput.,
187(2), pp. 777–784.

Atanackovic,
T. M.
, and
Stankovic,
B.
, 2008, “
On a Numerical Scheme for Solving Differential Equations of Fractional Order,” Mech. Res. Commun.,
35(7), pp. 429–438.

[CrossRef]
Kirk,
D.
, 2004, Optimal Control Theory: An Introduction,
Dover Publications, Mineola, NY.

El-Nabulsi,
R. A.
, 2005, “
A Fractional Action-like Variational Approach of Some Classical, Quantum and Geometrical Dynamics,” Int. J. Appl. Math.,
17(3), pp. 299–317.

El-Nabulsi,
R. A.
, and
Torres,
D. F. M.
, 2007, “
Necessary Optimality Conditions for Fractional Action-like Integrals of Variational Calculus With Riemann-Liouville Derivatives of Order (α, β),” Math. Methods Appl. Sci.,
30(15), pp. 1931–1939.

[CrossRef]
EL-Nabulsi,
A. R.
, 2009, “
Fractional Action-like Variational Problems in Holonomic, Non-Holonomic and Semi-Holonomic Constrained and Dissipative Dynamical Systems,” Chaos Solitons Fractals,
42(1), pp. 52–61.

[CrossRef]
Rakhshan,
S. A.
,
Effati,
S.
, and
Kamyad,
A. V.
, 2018, “
Solving a Class of Fractional Optimal Control Problems by the Hamilton-Jacobi-Bellman Equation,” J. Vib. Control,
24(9), pp. 1741–1756.

[CrossRef]
Almeida,
R.
,
Pooseh,
S.
, and
Torres,
D. F. M.
, 2015, Computational Methods in the Fractional Calculus of Variations,
Imperial College Press, London.

Yong,
J.
, and
Zhou,
X. Y.
, 1999, Stochastic Controls, Vol.
43 (Applications of Mathematics),
Springer-Verlag, New York.

Sun,
M.
, 1993, “
Domain Decomposition Algorithms for Solving Hamilton-Jacobi-Bellman Equations,” Numer. Funct. Anal. Optim.,
14(1–2), pp. 145–166.

[CrossRef]
Xu,
H.
,
Sun,
Z.
, and
Xie,
S.
, 2011, “
An Iterative Algorithm for Solving a Kind of Discrete HJB Equation With M-Functions,” Appl. Math. Lett.,
24(3), pp. 279–282.

[CrossRef]
Chen,
G.
, and
Chen,
G.
, 2011, “
A Numerical Algorithm Based on a Variational Iterative Approximation for the Discrete Hamilton-Jacobi-Bellman (HJB) Equation,” Comput. Math. Appl.,
61(4), pp. 901–907.

[CrossRef]
Zhou,
S.
, and
Zhan,
W.
, 2003, “
A New Domain Decomposition Method for an HJB Equation,” J. Comput. Appl. Math.,
159(1), pp. 195–204.

[CrossRef]