1. Agrawal, O.P. On a general formulation for the numerical solution of optimal control problems, Int. J. Control 50 (1989) 627–638.
2. Agrawal O.P. A general formulation and solution scheme for fractional optimal control problem, Nonlinear Dynam, 38 (2004) 323–337.
3. Agrawal, O.P. and Baleanu, D. A Hamiltonian formulation and a direct numerical scheme for fractional optimal control problems, J. Vib. Control. 13 (2007) 1269–1281.
4. Ahmadi Darani, M. and Saadatmandi, A. The operational matrix of fractional derivative of the fractional-order Chebyshev functions and its applications, Comput. Methods Differ. Equ. 5(1) (2017), 67–87.
5. Akbarian, T. and Keyanpour, M. A new approach to the numerical solution of fractional order optimal control problems, Appl. Appl. Math. 8(2) (2013), 523–534.
6. Ashpazzadeh, E., Lakestani, M. and Yildirim, A. Biorthogonal multiwavelets on the interval for solving multidimensional fractional optimal control problems with inequality constraint, Optimal Control Appl. Methods 41(5) (2020), 1477–1494.
7. AtanackoviÄ‡, T.M., PilipoviÄ‡, S., StankoviÄ‡, B., and Zorica, D. Fractional calculus with applications in mechanics. Wave propagation, impact and variational principles. Mechanical Engineering and Solid Mechanics Series, ISTE, London; John Wiley & Sons, Inc., Hoboken, NJ, 2014.
8. Bagley, RL and Torvik PJ (1983) A theoretical basis for the application of fractional calculus to viscoelasticity, J. Rheol., 27, 201–210.
9. Baleanu, D., Defterli, O. and Agrawal, O.P. A central difference numerical scheme for fractional optimal control problems, J. Vib. Control. 15(4) (2009) 583–597.
10. Bohannan, G.W. Analog fractional order controller in temperature and motor control applications, J. Vib. Control. 14(9-10) (2008) 1487–1498.
11. Caputo, M. Linear models of dissipation whose Q is almost frequency independent II, Reprinted from Geophys. J. R. Astr. Soc. 13 (1967), no. 5, 529–539. Fract. Calc. Appl. Anal. 11 (2008), no. 1, 4–14.
12. Chow, T.S. Fractional dynamics of interfaces between soft-nanoparticles and rough substrates, Phys. Lett. A, 342, (2005) 148–155.
13. Defterli, O. A numerical scheme for two-dimensional optimal control problems with memory effect, Comput. Math. Appl. 59(5) (2010) 1630–1636.
14. Garrappa, R. Numerical solution of fractional differential equations: A survey and a software tutorial, https://www.mdpi.com/2227-7390/6/2/16
15. Ghomanjani, F. A numerical technique for solving fractional optimal control problems and fractional Riccati differential equation, J. Egyptian Math. Soc. 24(4) (2016), 638–643.
16. Habibli, M. and Noori Skandari, M.H. Fractional Chebyshev pseudospectral method for fractional optimal control problems, Optimal Control Appl. Methods 40(3) (2019), 558–572.
17. Hoda F. Ahmed A numerical technique for solving multidimensional fractional optimal control problems, Journal of Taibah University for Science, 12(5), (2018) 494–505.
18. Keshavarz, E., Ordokhani, Y. and Razzaghi, M. A numerical solution for fractional optimal control problems via Bernoulli polynomials, 22(18) (2016), 3889–3903.
19. Jesus, I.S. and Machado, J.T. Fractional control of heat diffusion systems, Nonlinear Dyn. 54 (2008) 263–282.
20. Kreyszig, E. Introductory functional analysis with applications, New York: John Wiley and sons. Inc, 1978.
21. Kruchinin, D.V. Explicit formulas for some generalized Mott polynomials, Advanced Studies in Contemporary Mathematics, 24 (3) (2014) 327–332.
22. Lotfi, A., Dehghan, M. and Yousefi, S.A. A numerical technique for solving fractional optimal control problems,Comput. Math. with Appl. 62(2011) 1055–1067.
23. Maheswaran, A. and Elango, Characterization of delta operator for Euler, Bernoulli of second kind and moot polynomials, Int. J. Pure Appl. Math. 109 (2) 2016, (2016) 371–384.
24. Moghaddam, M.A., Yousef, E. and Lakestani, M. Solving fractional optimal control problems using Genocchi polynomials, Comput. Methods Differ. Equ. 9(1) (2021), 79–93.
25. Mott, N.F. The polarization of electrons by double scattering, Proc. R. Soc. Lond. A 135, (1932) 429–458.
26. Nemati. A., Yousefi, S.A. A numerical method for solving fractional optimal control problems using Ritz method, J. Comput. Nonlinear Dyn. 11(5) 051015-1 (2016) 7 pp.
27. Oldham, K.B. and Spanier, J. The fractional calculus: Theory and application of differentiation and integration to arbitrary order, Acad. Press, N. York and London, 1974.
28. Ross, B. A brief history and exposition of the fundamental theory of fractional calculus, in fractional calculus and its Applications, Lecture Notes in Mathematics, Vol.457, pp. 1–36, Springer, Berlin, 1975.
29. Weisstein, Eric W. “Mott Polynomial.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/MottPolynomial
30. Yari A Numerical solution for fractional optimal control problems by Hermite polynomials, J. Vib. Control. 25 (2021) 5–6.
31. Yousefi, S.A., Lotfi, A. and Dehghan, M. The use of a Legendre multiwavelet collocation method for solving the fractional optimal control problems, J. Vib. Control. 17(13)(2011) 2059–2065.
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