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Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics

Author

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  • Tatiana Odzijewicz
  • Agnieszka B. Malinowska
  • Delfim F. M. Torres

Abstract

We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the basic and isoperimetric problems, as well as natural boundary conditions for free-boundary value problems. The fractional action-like variational approach (FALVA) is extended and some applications to physics discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlaaa:871912
    DOI: 10.1155/2012/871912
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    Cited by:

    1. 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.
    2. Baba, Bashir Abdullahi & Bilgehan, Bulent, 2021. "Optimal control of a fractional order model for the COVID – 19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Goel, Eti & Pandey, Rajesh K. & Yadav, S. & Agrawal, Om P., 2023. "A numerical approximation for generalized fractional Sturm–Liouville problem with application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 417-436.
    4. Muhammad Imran Asjad & Saif Ur Rehman & Ali Ahmadian & Soheil Salahshour & Mehdi Salimi, 2021. "First Solution of Fractional Bioconvection with Power Law Kernel for a Vertical Surface," Mathematics, MDPI, vol. 9(12), pages 1-18, June.

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