IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v174y2017i1d10.1007_s10957-016-0883-4.html
   My bibliography  Save this article

Variational Problems Involving a Caputo-Type Fractional Derivative

Author

Listed:
  • Ricardo Almeida

    (University of Aveiro)

Abstract

The aim of this paper is to study certain problems of calculus of variations that are dependent upon a Lagrange function on a Caputo-type fractional derivative. This type of fractional operator is a generalization of the Caputo and the Caputo–Hadamard fractional derivatives that are dependent on a real parameter $$\rho $$ ρ . Sufficient and necessary conditions of the first and second order are presented. The cases of integral and holonomic constraints are also considered.

Suggested Citation

  • Ricardo Almeida, 2017. "Variational Problems Involving a Caputo-Type Fractional Derivative," Journal of Optimization Theory and Applications, Springer, vol. 174(1), pages 276-294, July.
  • Handle: RePEc:spr:joptap:v:174:y:2017:i:1:d:10.1007_s10957-016-0883-4
    DOI: 10.1007/s10957-016-0883-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-016-0883-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s10957-016-0883-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Harendra Singh & Rajesh K. Pandey & Hari Mohan Srivastava, 2019. "Solving Non-Linear Fractional Variational Problems Using Jacobi Polynomials," Mathematics, MDPI, vol. 7(3), pages 1-24, February.
    2. Almeida, Ricardo & Morgado, M. Luísa, 2018. "The Euler–Lagrange and Legendre equations for functionals involving distributed–order fractional derivatives," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 394-403.
    3. Muath Awadalla & Kinda Abuasbeh & Muthaiah Subramanian & Murugesan Manigandan, 2022. "On a System of ψ -Caputo Hybrid Fractional Differential Equations with Dirichlet Boundary Conditions," Mathematics, MDPI, vol. 10(10), pages 1-15, May.
    4. Loïc Bourdin & Rui A. C. Ferreira, 2021. "Legendre’s Necessary Condition for Fractional Bolza Functionals with Mixed Initial/Final Constraints," Journal of Optimization Theory and Applications, Springer, vol. 190(2), pages 672-708, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:174:y:2017:i:1:d:10.1007_s10957-016-0883-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.