On exact solutions of a class of fractional Euler-lagrange equations

Nonlinear Dynamics

Volumn 52, Issue 4, 2008, Pages 331-335

  Baleanu, Dumitru ^a,b   Trujillo, Juan J ^c  

^a INSTITUTE OF SPACE SCIENCES   (Romania)

^b CANKAYA UNIVERSITY   (Turkey)

^c UNIVERSIDAD DE LA LAGUNA   (Spain)

Author keywords

Differential equations of fractional order; Fractional calculus; Fractional variational calculus

Indexed keywords

DIFFERENTIAL EQUATIONS; EULER EQUATIONS; FUNCTION EVALUATION; LAGRANGE MULTIPLIERS; VARIATIONAL TECHNIQUES;

DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER; FRACTIONAL CALCULUS; FRACTIONAL VARIATIONAL CALCULUS;

NONLINEAR EQUATIONS;

EID: 42449096849     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-007-9281-7     Document Type: Article

References (28)

1. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)
2. Zaslavsky, G.M.: Hamiltonian Chaos and Fractional Dynamics. Oxford University Press, Oxford (2005)
3. Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam (2006)
4. Magin, R.L.: Fractional Calculus in Bioengineering. Begell House, Connecticut (2006)
5. Mainardi, F., Luchko, Yu., Pagnini, G.: The fundamental solution of the space-time fractional diffusion equation. Frac. Calc. Appl. Anal. 4(2), 153 (2001)
6. Tenreiro Machado, J.A.: A probabilistic interpretation of the fractional-order differentiation. Frac. Calc. Appl. Anal. 8, 73-80 (2003)
7. Tenreiro Machado, J.A.: Discrete-time fractional-order controllers. Frac. Calc. Appl. Anal. 4, 47-66 (2001)
8. Tofighi, A.: The intrinsic damping of the fractional oscillator. Phys. A 329, 29-34 (2006)
9. Trujillo, J.J.: On a Riemann-Liouville generalized Taylor's formula. J. Math. Anal. Appl. 231, 255-265 (1999)
10. Lim, S.C., Muniady, S.V.: Stochastic quantization of nonlocal fields. Phys. Lett. A 324, 396-405 (2004)
11. Stanislavsky, A.A.: Fractional oscillator. Phys. Rev. E 70, 051103 (2004)
12. Riewe, F.: Nonconservative Lagrangian and Hamiltonian mechanics. Phys. Rev. E 53, 1890-1899 (1996)
13. Riewe, F.: Mechanics with fractional derivatives. Phys. Rev. E 55, 3581-3592 (1997)
14. Klimek, M.: Fractional sequential mechanics-models with symmetric fractional derivatives. Czech. J. Phys. 51, 1348-1354 (2001)
15. Klimek, M.: Lagrangian and Hamiltonian fractional sequential mechanics. Czech. J. Phys. 52, 1247-1253 (2002)
16. El-Nabulusi, R.A.: A fractional approach to nonconservative Lagrangian dynamics. Fiz. A 14(4), 289-298 (2005)
17. Agrawal, O.P.: Formulation of Euler-Lagrange equations for fractional variational problems. J. Math. Anal. Appl. 272, 368-379 (2002)
18. Agrawal, O.P.: Fractional variational calculus and the transversality conditions. J. Phys. A: Math. Gen. 39, 10375-10384 (2006)
19. Agrawal, O.P.: Generalized Euler-Lagrange equations and transversality conditions for FVPs in terms of Caputo Derivative. In: Tas, K., Tenreiro Machado, J.A., Baleanu, D. (eds.) Proc. MME06, Ankara, Turkey, 27-29 April 2006, to appear in J. Vib. Control (2007)
20. Rabei, E.M., Nawafleh, K.I., Hijjawi, R.S., Muslih, S.I. Baleanu, D.: The Hamiltonian formalism with fractional derivatives. J. Math. Anal. Appl. 327, 891-897 (2007)
21. Muslih, S., Baleanu, D.: Hamiltonian formulation of systems with linear velocities within Riemann-Liouville fractional derivatives. J. Math. Anal. Appl. 304(3), 599-603 (2005)
22. Baleanu, D.: Fractional Hamiltonian analysis of irregular systems. Signal Process. 86(10), 2632-2636 (2006)
23. Baleanu, D., Muslih, S.I.: Formulation of Hamiltonian equations for fractional variational problems. Czech. J. Phys. 55(6), 633-642 (2005)
24. Baleanu, D., Muslih, S.: Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives. Phys. Scr. 72(2-3), 119-121 (2005)
25. Baleanu, D., Avkar, T.: Lagrangians with linear velocities within Riemann-Liouville fractional derivatives. Nuovo Cimento B 119, 73-79 (2004)
26. Tenreiro-Machado, J.A.: Discrete-time fractional-order controllers. Frac. Calc. Appl. Anal. 4(1), 47-68 (2001)
27. Agrawal, O.P., Baleanu, D.: A Hamiltonian formulation and a direct numerical scheme for fractional optimal control problems. In: Tas, K., Tenreiro Machado, J.A., Baleanu, D. (eds.) Proc. MME06, Ankara, Turkey, 27-29 April 2006, to appear in J. Vib. Control (2007)
28. Jumarie, G.: Lagrangian mechanics of fractional order, Hamilton-Jacobi fractional PDE and Taylor's series of nondifferntiable functions. Chaos Solitons Fractals 32, 969-987 (2007)