THERMAL SCIENCE

International Scientific Journal

Jing Li Fu

,

Lijun Zhang

,

Chaudry Masood Khalique

,

Ma Li Guo

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
circulatory integral, Routh's equation, Lagrange system, Riemann-Liouville fractional derivatives
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
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Issue 2, PAGES [1355 - 1363]
REFERENCES
  1. Hilfer, R., Applications of Fractional Calculus in Physics, World Scientific, Singapore, Singapore, 2000
  2. Zaslavsky, G. M., Hamiltonian Chaos and Fractional Dynamics, Oxford University Press, Oxford, UK, 2005
  3. Naber, M., Time Fractional Schrodingere Equation, Journale Math. Phys., 45 (2004), 8, pp. 3339-3352
  4. Surguladze, T. A., On Certain Applications of Fraction Calculus to Viscoelasticity, Journal Math. Sciences, 112 (2002), 112, pp. 4517-4557
  5. Zhang, L., et al., Bifurcations and Exact Traveling Wave Solutions of the Zakharov-Rubenchik Equation, Disc. Cont. Dyna. Syst., 13 (2020), 10, pp. 2927-2939
  6. Podlubny, I., Fractional Differential Equations, Academic Press, New York, USA, 1999
  7. Riewe, F., Nonconservative Lagrangian and Hamiltonian Mechanics, Phys. Review E, 53 (1996), pp. 1890-1899
  8. Agrawal, O. P., Formulation of Euler-Lagrange Equations for Variational Problems, Journal Math. Anal. Appl., 272 (2002), 1, pp. 368-379
  9. Zhou, S., et al., Langrage Equations of Non-Holonomic Systems with Fractional Derivatives, Chinese Phys. B, 19 (2010), 120310
  10. Lacroix, S. F., Traite du calcul diffrentiel et du calcul integral, Courcier Paris (in Franch), France, 1819
  11. Kilbas, A. A., et al., Theory and Applications of Fractional Differential Equations, Elsevier, New York, USA, 2006
  12. Ahn, H. S., et al., Robust Stability Test of a Class of Linear Time Invariant Interval Fractional-Order System Using Lyapunov Inequality, Appl. Math. Comp., 187 (2007), 1, pp. 27-34
  13. Shahin, A. M., et al., On Fractional Order Quantum Mechanics, Int. J. Non-linear Sci., 4 (2009), 4, pp. 469-472
  14. Podlubny, I., Fractional Differential Equations, Academic Press, New York, USA, 1999
PDF VERSION [DOWNLOAD]
Circulatory integral and Routh's equations of Lagrange systems with Riemann-Liouville fractional derivatives

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence