THERMAL SCIENCE

International Scientific Journal

Thermal Science - Online First

online first only

Circulatory integral and Routh's equations of Lagrange systems with Riemann-Liouville fractional derivatives

ABSTRACT
In this paper, the circulatory integral and Routh's equations of Lagrange systems are established with Riemann-Liouville fractional derivatives, and the circulatory integral of Lagrange systems is obtained by making use of the relationship between Riemann-Liouville fractional integrals and fractional derivatives. Thereafter, the Routh's equations of Lagrange systems are given based on the fractional circulatory integral. Two examples are presented to illustrate the application of the results.
KEYWORDS
PAPER SUBMITTED: 2020-05-20
PAPER REVISED: 2020-06-20
PAPER ACCEPTED: 2020-06-20
PUBLISHED ONLINE: 2021-01-31
DOI REFERENCE: https://doi.org/10.2298/TSCI200520034F
REFERENCES
  1. Hilfer R. Applications of Fractional Calculus in Physics. World Scientific, Singapore, 2000
  2. Zaslavsky G M. Hamiltonian Chaos and Fractional Dynamics. Oxford: Oxford University Press, 2005
  3. Naber M. Time fractional Schrodinger equation. J. Math. Phys., 2004, 45, 3339-3352
  4. Surguladze T A. On certain applications of fraction calculus to viscoelasticity. J. Math. Sciences, 2002, 112, 4517-4557
  5. L. Zhang, P. Yuan, J. Fu, C M Khalique. Bifurcations and exact traveling wave solutions of the Zakharov-Rubenchik equation. Disc. Cont. Dyna. Syst. - S, doi: 10.3934/dcdss.2020214
  6. Igor Podlubny. Fractional Differential Equations. Academic Press, 1999
  7. Riewe F. Lagrangian formulation of classical fields within Riemann-Liouvile fractional derivatives. Phys. Review E, 1996, 53,1890
  8. Agrawal O P. Formulation of Euler-Lagrange equations for variational problems. J. Math. Anal. Appl., 2002, 272, 368-379
  9. Zhou S, Fu J L, Liu Y S. Langrage equations of nonholonomic systems with fractional derivatives. Chinese Phys. B, 2010, 19,120310
  10. Lacroix S F.Traite du calcul diffrentiel et du calcul integral. Courcier Paris, 1819
  11. Kilbas A A, Rivastava M, Trujillo J J. Theory and Applications of Fractional Differential Equations. Elsevier, 2006
  12. Ahn H S, Chen Y Q, Podlubny I. Robust stability test of a class of linear time invariant interval fractional-order system using Lyapunov inequality. Appl. Math. Comp., 2007, 187, 27-34
  13. Shahin A M, Ahmed E, Omar Yassmin A. On fractional order quantum mechanics.Int. J. Nonlinear Sci., 2009, 4, 469-472
  14. Igor Podlubny. Fractional Differential Equations. Academic Press, 1999