Higher-order Hahn's quantum variational calculus

Nonlinear Analysis, Theory, Methods and Applications

Volumn 75, Issue 3, 2012, Pages 1147-1157

  Brito Da Cruz, Artur M C ^a   Martins, Natália ^b   Torres, Delfim F M ^b  

^a INSTITUTO POLITÉCNICO DE SETÚBAL   (Portugal)

^b UNIVERSITY OF AVEIRO   (Portugal)

Author keywords

EulerLagrange equations; Hahn's calculus; q differences

Indexed keywords

EULER-LAGRANGE; EULER-LAGRANGE EQUATIONS; HAHN'S CALCULUS; HIGHER ORDER; NECESSARY OPTIMALITY CONDITION; Q-DIFFERENCES; VARIATIONAL PROBLEMS;

VARIATIONAL TECHNIQUES;

CALCULATIONS;

EID: 82155164176     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2011.01.015     Document Type: Article

References (26)

1. R.P. Feynman, and A.R. Hibbs Quantum Mechanics and Path Integrals 1965 McGraw-Hill
2. R.A.C. Ferreira, and D.F.M. Torres Higher-order calculus of variations on time scales Mathematical Control Theory and Finance 2008 Springer Berlin 149 159
3. A.B. Malinowska, and D.F.M. Torres Strong minimizers of the calculus of variations on time scales and the Weierstrass condition Proc. Estonian Acad. Sci. 58 4 2009 205 212
4. N. Martins, and D.F.M. Torres Calculus of variations on time scales with nabla derivatives Nonlinear Anal. 71 12 2009 e763 e773
5. R. Almeida, A.B. Malinowska, and D.F.M. Torres A fractional calculus of variations for multiple integrals with application to vibrating string J. Math. Phys. 51 3 2010 033503 (12 pp)
6. R.A. El-Nabulsi, and D.F.M. Torres 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 2007 1931 1939 (Pubitemid 47395843)
7. G.S.F. Frederico, and D.F.M. Torres Fractional conservation laws in optimal control theory Nonlinear Dynam. 53 3 2008 215 222
8. G. Bangerezako Variational q-calculus J. Math. Anal. Appl. 289 2 2004 650 665 (Pubitemid 38131001)
9. J. Cresson, G.S.F. Frederico, and D.F.M. Torres Constants of motion for non-differentiable quantum variational problems Topol. Methods Nonlinear Anal. 33 2 2009 217 231
10. A.B. Malinowska, and D.F.M. Torres The Hahn quantum variational calculus J. Optim. Theory Appl. 147 3 2010 419 442
11. T. Ernst The different tongues of q-calculus Proc. Estonian Acad. Sci. 57 2 2008 81 99
12. V. Kac, and P. Cheung Quantum Calculus 2002 Springer New York
13. R. Almeida, and D.F.M. Torres Hölderian variational problems subject to integral constraints J. Math. Anal. Appl. 359 2 2009 674 681
14. W. Hahn ber orthogonalpolynome, die q-Differenzengleichungen gengen Math. Nachr. 2 1949 4 34
15. R. lvarez-Nodarse On characterizations of classical polynomials J. Comput. Appl. Math. 196 1 2006 320 337
16. A. Dobrogowska, and A. Odzijewicz Second order q-difference equations solvable by factorization method J. Comput. Appl. Math. 193 1 2006 319 346
17. ω-orthogonal polynomials J. Comput. Appl. Math. 205 1 2007 314 324 (Pubitemid 46636074)
18. K.A. Aldwoah, Generalized time scales and associated difference equations, Ph.D. Thesis, Cairo University, 2009.
19. K.A. Aldwoah, and A.E. Hamza Difference time scales Int. J. Math. Stat. 9 A11 2011 106 125
20. M.H. Annaby, A.E. Hamza, K.A. Aldwoah, Hahn difference operator and associated JacksonNörlund integrals. Preprint.
21. N.R.O. Bastos, R.A.C. Ferreira, and D.F.M. Torres Discrete-time fractional variational problems Signal Process. 91 3 2011 513 524
22. W.G. Kelley, and A.C. Peterson Difference Equations 1991 Academic Press Boston, MA
23. A.B. Malinowska, and D.F.M. Torres On the diamond-alpha Riemann integral and mean value theorems on time scales Dynam. Systems Appl. 18 3-4 2009 469 481
24. D. Mozyrska, Ewa Pawuszewicz, and D.F.M. Torres The RiemannStieltjes integral on time scales Aust. J. Math. Anal. Appl. 7 1 2010 Art. 10, 14 pp
25. B. van Brunt The Calculus of Variations 2004 Springer New York
26. R. Almeida, and D.F.M. Torres Generalized EulerLagrange equations for variational problems with scale derivatives Lett. Math. Phys. 92 3 2010 221 229