Necessary optimality conditions for fractional action-like integrals of variational calculus with Riemann-Liouville derivatives of order (α, β)

Mathematical Methods in the Applied Sciences

Volumn 30, Issue 15, 2007, Pages 1931-1939

  El Nabulsi, Rami Ahmad ^a   Torres, Delfim F M ^b  

^a Jeju National University   (South Korea)

^b UNIVERSITY OF AVEIRO   (Portugal)

Author keywords

Fractional action like variational approach; Fractional constants of motion; Fractional Euler Lagrange equations

Indexed keywords

DIFFERENTIATION (CALCULUS); EULER EQUATIONS; LAGRANGE MULTIPLIERS;

FRACTIONAL ACTION-LIKE VARIATIONAL APPROACH; FRACTIONAL CONSTANTS OF MOTION; FRACTIONAL EULER-LAGRANGE EQUATIONS; RIEMANN-LIOUVILLE DERIVATIVES;

INTEGRAL EQUATIONS;

EID: 34548583736     PISSN: 01704214     EISSN: 10991476     Source Type: Journal    
DOI: 10.1002/mma.879     Document Type: Article

References (22)

1. Carpinteri A, Mainardi F. Fractals and Fractional Calculus in Continuum Mechanics. Springer: Berlin, 1997.
2. Srivastava HM, Owa S (eds). Univalent Functions, Fractional Calculus and their Applications. Wiley: New York, 1989.
3. West BJ, Grigolini P. Applications of Fractional Calculus in Physics. World Scientific: Singapore, 1998.
4. Riewe F. Nonconservative Lagrangian and Hamiltonian mechanics. Physical Review E 1996; 53:1890-1899. DOI:10.1103/PhysRevE.53.1890
5. Klimek M. Fractional sequential mechanics models with symmetric fractional derivative. Czechoslovak Journal of Physics 2001; 51(12):1348-1354. DOI:10.1023/A:1013378221617
6. Agrawal OP. Formulation of Euler-Lagrange equations for fractional variational problems. Journal of Mathematical Analysis and Applications 2002; 272:368-379. DOI:10.1016/S0022-247X(02)00180-4
7. Baleanu D, Avkar T. Lagrangians with linear velocities within Riemann-Liouville fractional derivatives. Nuovo Cimento 2004; 119:73-79.
8. Klimek M. Lagrangian fractional mechanics - a noncommutative approach. Czechoslovak Journal of Physics 2005; 55(11):1447-1453. DOI:10.1007/s10582-006-0024-7
9. El-Nabulsi RA. A fractional approach of nonconservative Lagrangian dynamics. Fizika A 2005; 14(4):289-298.
10. El-Nabulsi RA. A fractional action-like variational approach of some classical, quantum and geometrical dynamics. International Journal of Applied Mathematics 2005; 17(3):299-317.
11. Oldham KB, Spanier J. The Fractional Calculus. Academic Press: New York, 1974.
12. Podlubny I. Fractional Differential Equations. Academic Press: New York, 1999.
13. Samko SG, Kilbas AA, Marichev 01. Fractional Integrals and Derivatives. Gordon and Breach: Amsterdam, 1993.
14. Cresson J. Fractional embedding of differential operators and Lagrangian systems. Journal of Mathematical Physics 2007; 48(3). DOI:10.1063/1.2483292
15. Cresson J, Darses S. Plongement stochastique des systèmes Lagrangiens [Stochastic embedding of Lagrangian systems]. Comptes Rendus Mathematique de l'Académie des Sciences de Paris 2006; 342(5):333-336. DOI:10.1016/j.crma.2005.12.028
16. Udriste C. Multi-time maximum principle. Short Communication at International Congress of Mathematicians (ICM 2006). European Mathematical Society: Madrid. 22-30 August 2006; 547.
17. El-Nabulsi RA. Some geometrical aspects of nonconservative autonomous Hamiltonian dynamical systems. International Journal of Applied Mathematics and Statistics 2006; 5(S06):50-61.
18. Frederico GSF, Torres DFM. Noether's theorem for fractional optimal control problems. Proceedings of the 2nd IFAC Workshop on Fractional Differentiation and its Applications, Porto, 19-21 July 2006; 142-147.
19. Frederico GSF, Torres DFM. Constants of motion for fractional action-like variational problems. International Journal of Applied Mathematics 2006; 19(1):97-104.
20. Frederico GSF, Torres DFM. A formulation of Noether's theorem for fractional problems of the calculus of variations. Journal of Mathematical Analysis and Applications 2007. DOI:10.1016/j.jmaa.2007.01.013
21. Muslih S, Baleanu D. Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives. Journal of Mathematical Analysis and Applications 2005; 304:599-606. DOI:10.1016/j.jmaa.2004.09.043
22. Stanislavsky AA. Hamiltonian formalism of fractional systems. European Physical Journal B 2006; 49:93-101. DOI:10.1140/epjb/e2006-00023-3