Necessary optimality conditions for fractional action-like problems with intrinsic and observer times

WSEAS Transactions on Mathematics

Volumn 7, Issue 1, 2008, Pages 6-11

  Frederico, Gastão S F ^a   Torres, Delfim F M ^b  

^a University of Cape Verde   (Cape Verde)

^b UNIVERSITY OF AVEIRO   (Portugal)

Author keywords

Calculus of variations; FALVA problems; Higher order DuBois Reymond stationary condition; Higher order Euler Lagrange equations; Multi time control theory

Indexed keywords

HIGHER ORDER; LAG RANGE; NECESSARY OPTIMALITY CONDITIONS; OBSERVER (OBS); OPTIMAL CONTROL PROBLEM (OCP); STATIONARY CONDITIONS; VARIATIONAL PROBLEMS;

EID: 47049086566     PISSN: 11092769     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (17)

1. O. P. Agrawal. Formulation of Euler-Lagrange equations for fractional variational problems, J. Math. Anal. Appl. 272 (2002), no. 1, 368-379.
2. O. P. Agrawal. A general formulation and solution scheme for fractional optimal control problems, Nonlinear Dynam. 38 (2004), no. 1-4, 323-337.
3. D. Baleanu, T. Avkar. Lagrangians witb linear velocities within Riemann-Liouville fractional derivatives, Nuovo Cimento 119 (2004) 73-79.
4. J. Cresson. Fractional embedding of differential operators and Lagrangean systems, J. Math. Phys., 48 (2007), no. 3, 033504, 34 pp.
5. I. Duca, C. Udriste. Some inequalities satisfied by periodical solutions of multi-time Hamilton equations, Balkan J. of Geometry and Its Applications 11 (2006), no. 2, 50-60.
6. R. A. El-Nabulsi. A fractional action-like variational approach of some classical, quantum and geometrical dynamics, Int. J. Appl. Math. 17 (2005), 299-317.
7. R. A. El-Nabulsi. A fractional approach to nonconservative lagrangian dynamical systems, FIZIKA A 14 (2005), no. 4, 289-298.
8. R. A. E;-Nabulsi, D. F. M. Torres. Necessary Optimality Conditions for Fractional Action-Like Integrals of Variational Calculus with Riemann-Liouville Derivatives of Order (α, β), Math. Meth. Appl. Sci. 30 (2007), no. 15, 1931-1939.
9. G. S. F. Frederico, D. F. M. Torres. Noether's theorem for fractional optimal control problems, Proc. 2nd IFAC Workshop on Fractional Differentiation and its Applications, 19-21 July 2006, Porto, 142-147.
10. G. S. F. Frederico, D. F. M. Torres. A formulation of Noether's theorem for fractional problems of the calculus of variations, J. Math. Anal. Appl. 334 (2007), no. 2, 834-846.
11. G. Jumarie. Fractional Hamilton-Jacobi equation for the optimal control of nonrandom fractional dynamics with fractional cost function, J. Appl. Math. and Computing 23 (2007), no. 1-2, 215-228.
12. M. Klimek. Lagrangean and Hamiltonian fractional sequential mechanics, Czechoslovak J. Phys. 52 (2002), no. 11, 1247-1253.
13. M. Klimek. Lagrangian fractional mechanics - a noncommutative approach, Czechoslovak J. Phys. 55 (2005), no. 11, 1447-1453.
14. F. Riewe. Nonconservative Lagrangian and Hamiltonian mechanics, Phys. Rev. E (3) 53 (1996), no. 2, 1890-1899.
15. D. F. M. Torres. Proper extensions of Noether's symmetry theorem for nonsmooth extremals of the calculus of variations, Commun. Pure Appl. Anal. 3 (2004), no. 3, 491-500.
16. C. Udriste, I. Duca. Periodical solutions of multi-time Hamilton equations, Analele Universitatii Bucuresti 55 (2005), no. 1, 179-188.
17. C. Udriste, I. Tevy. Multi-time Euler-Lagrange-Hamilton theory, WSEAS Transactions on Mathematics 6 (2007), no. 6, 701-709.