Higher order fractional variational optimal control problems with delayed arguments. (English) Zbl 1244.49028
Summary: This article deals with higher order Caputo fractional variational problems in the presence of delay in the state variables and their integer higher order derivatives.
MSC:
| 49J99 | Existence theories in calculus of variations and optimal control |
| 26A33 | Fractional derivatives and integrals |
References:
| [1] | Kilbas, A. A.; Srivastava, H. H.; Trujillo, J. J., Theory and Applications of Fractional Differential Equations (2006), Elsevier: Elsevier Amsterdam · Zbl 1092.45003 |
| [2] | Samko, S. G.; Kilbas, A. A.; Marichev, O. I., Fractional Integrals and Derivatives - Theory and Applications (1993), Gordon and Breach: Gordon and Breach Linghorne, P.A. · Zbl 0818.26003 |
| [3] | Magin, R. L., Fractional Calculus in Bioengineering (2006), Begell House Publisher, Inc: Begell House Publisher, Inc Connecticut |
| [4] | Heymans, N.; Podlubny, I., Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives, Rheol. Acta, 45, 765-771 (2006) |
| [5] | Jesus, I. S.; Machado, J. A.T., Fractional control of heat diffusion system, Nonlinear Dynam., 54, 3, 263-282 (2008) · Zbl 1210.80008 |
| [6] | Baleanu, D.; Maraaba, T.; Jarad, F., Fractional principles with delay, J. Phys. A: Math. Theor., 41 (2008) · Zbl 1141.49321 |
| [7] | Jarad, F.; Maraaba, T.; Baleanu, D., Fractional variational principles with delay within Caputo derivatives, Rep. Math. Phys., 65, 1, 17-28 (2010) · Zbl 1195.49030 |
| [8] | Mainardi, F.; Luchko, Y.; Pagnini, G., The fundamental solution of the space-time fractional the space-time fractional diffusion equation, Frac. Calc. Appl. Anal., 4, 2, 153-192 (2001) · Zbl 1054.35156 |
| [9] | Scalas, E.; Gorenflo, R.; Mainardi, F., Uncoupled continuous-time random walks: solution and limiting behavior of the master equation, Phys. Rev. E, 69, 011107-1 (2004) |
| [10] | li, C. P.; Zhao, Z. G., Introduction to fractional integrability and differentiability, Eur. Phys. J. Special Topics, 193, 5-26 (2011) |
| [11] | Agrawal, O. P.; Baleanu, D., Hamiltonian formulation and a direct numerical scheme for fractional optimal control problems, J. Vib. Control, 13, 9-10, 1269-1281 (2007) · Zbl 1182.70047 |
| [12] | Chen, Y. Q.; Vinagre, B. M.; Podlubny, I., Continued fraction expansion approaches to discretizing fractional order derivatives-an expository review, Nonlinear Dynam., 38, 1-4, 155-170 (2004) · Zbl 1134.93300 |
| [13] | Rosenblueth, J. F., Systems with time delay in the calculus of variations: a variational approach, J. Math. Control Inf., 5, 2, 125-145 (1988) · Zbl 0655.49017 |
| [14] | Tarasov, V. E.; Zaslavsky, G. M., Nonholonomic constraints with fractional derivatives, J. Phys. A: Math. Gen., 39, 31, 9797-9815 (2006) · Zbl 1101.70011 |
| [15] | Agrawal, O. P., A general formulation and solution scheme for fractional optimal control problems, Nonlinear Dynam., 38, 323-337 (2004) · Zbl 1121.70019 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
