IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i14p1665-d594925.html
   My bibliography  Save this article

Variational Problems with Time Delay and Higher-Order Distributed-Order Fractional Derivatives with Arbitrary Kernels

Author

Listed:
  • Fátima Cruz

    (Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
    These authors contributed equally to this work.)

  • Ricardo Almeida

    (Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
    These authors contributed equally to this work.)

  • Natália Martins

    (Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
    These authors contributed equally to this work.)

Abstract

In this work, we study variational problems with time delay and higher-order distributed-order fractional derivatives dealing with a new fractional operator. This fractional derivative combines two known operators: distributed-order derivatives and derivatives with respect to another function. The main results of this paper are necessary and sufficient optimality conditions for different types of variational problems. Since we are dealing with generalized fractional derivatives, from this work, some well-known results can be obtained as particular cases.

Suggested Citation

  • Fátima Cruz & Ricardo Almeida & Natália Martins, 2021. "Variational Problems with Time Delay and Higher-Order Distributed-Order Fractional Derivatives with Arbitrary Kernels," Mathematics, MDPI, vol. 9(14), pages 1-18, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:14:p:1665-:d:594925
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/14/1665/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/14/1665/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jozef Džurina & Said R. Grace & Irena Jadlovská & Tongxing Li, 2020. "Oscillation criteria for second‐order Emden–Fowler delay differential equations with a sublinear neutral term," Mathematische Nachrichten, Wiley Blackwell, vol. 293(5), pages 910-922, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Osama Moaaz & Ali Muhib & Shyam S. Santra, 2021. "An Oscillation Test for Solutions of Second-Order Neutral Differential Equations of Mixed Type," Mathematics, MDPI, vol. 9(14), pages 1-14, July.
    2. Shyam Sundar Santra & Abhay Kumar Sethi & Osama Moaaz & Khaled Mohamed Khedher & Shao-Wen Yao, 2021. "New Oscillation Theorems for Second-Order Differential Equations with Canonical and Non-Canonical Operator via Riccati Transformation," Mathematics, MDPI, vol. 9(10), pages 1-11, May.
    3. Grace, Said R. & Negi, Shekhar Singh & Abbas, Syed, 2022. "New oscillatory results for non-linear delay dynamic equations with super-linear neutral term," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    4. Shyam Sundar Santra & Omar Bazighifan & Mihai Postolache, 2021. "New Conditions for the Oscillation of Second-Order Differential Equations with Sublinear Neutral Terms," Mathematics, MDPI, vol. 9(11), pages 1-9, May.
    5. Yingzhu Wu & Yuanhong Yu & Jinsen Xiao, 2022. "Oscillation of Second Order Nonlinear Neutral Differential Equations," Mathematics, MDPI, vol. 10(15), pages 1-12, August.
    6. Yang-Cong Qiu & Kuo-Shou Chiu & Said R. Grace & Qingmin Liu & Irena Jadlovská, 2021. "Oscillation of Solutions to Third-Order Nonlinear Neutral Dynamic Equations on Time Scales," Mathematics, MDPI, vol. 10(1), pages 1-12, December.

    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:gam:jmathe:v:9:y:2021:i:14:p:1665-:d:594925. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.