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Fractional Herglotz variational principles with generalized Caputo derivatives

Author

Listed:
  • Garra, Roberto
  • Taverna, Giorgio S.
  • Torres, Delfim F.M.

Abstract

We obtain Euler–Lagrange equations, transversality conditions and a Noether-like theorem for Herglotz-type variational problems with Lagrangians depending on generalized fractional derivatives. As an application, we consider a damped harmonic oscillator with time-depending mass and elasticity, and arbitrary memory effects.

Suggested Citation

  • Garra, Roberto & Taverna, Giorgio S. & Torres, Delfim F.M., 2017. "Fractional Herglotz variational principles with generalized Caputo derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 94-98.
    • Handle: RePEc:eee:chsofr:v:102:y:2017:i:c:p:94-98
    DOI: 10.1016/j.chaos.2017.04.035
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    References listed on IDEAS

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    1. Tatiana Odzijewicz & Agnieszka B. Malinowska & Delfim F. M. Torres, 2012. "Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-24, May.
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    Cited by:

    1. Ding, Juan-Juan & Zhang, Yi, 2020. "Noether’s theorem for fractional Birkhoffian system of Herglotz type with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Huang, Li-Qin & Zhang, Yi, 2024. "Herglotz-type vakonomic dynamics and Noether theory of nonholonomic systems with delayed arguments," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    3. Vasily E. Tarasov, 2023. "General Fractional Noether Theorem and Non-Holonomic Action Principle," Mathematics, MDPI, vol. 11(20), pages 1-35, October.
    4. Tian, Xue & Zhang, Yi, 2019. "Noether’s theorem for fractional Herglotz variational principle in phase space," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 50-54.
    5. Salahshour, Soheil & Ahmadian, Ali & Allahviranloo, Tofigh, 2021. "A new fractional dynamic cobweb model based on nonsingular kernel derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    6. Salahshour, S. & Ahmadian, A. & Abbasbandy, S. & Baleanu, D., 2018. "M-fractional derivative under interval uncertainty: Theory, properties and applications," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 84-93.

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