IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i6p1037-d376076.html
   My bibliography  Save this article

Oscillatory Behavior of a Type of Generalized Proportional Fractional Differential Equations with Forcing and Damping Terms

Author

Listed:
  • Jehad Alzabut

    (Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
    These authors contributed equally to this work.)

  • James Viji

    (Department of Mathematics, Periyar University, Salem 636 011, Tamilnadu, India
    These authors contributed equally to this work.)

  • Velu Muthulakshmi

    (Department of Mathematics, Periyar University, Salem 636 011, Tamilnadu, India
    These authors contributed equally to this work.)

  • Weerawat Sudsutad

    (Department of General Education, Navamindradhiraj University, Bangkok 10300, Thailand
    These authors contributed equally to this work.)

Abstract

In this paper, we study the oscillatory behavior of solutions for a type of generalized proportional fractional differential equations with forcing and damping terms. Several oscillation criteria are established for the proposed equations in terms of Riemann-Liouville and Caputo settings. The results of this paper generalize some existing theorems in the literature. Indeed, it is shown that for particular choices of parameters, the obtained conditions in this paper reduce our theorems to some known results. Numerical examples are constructed to demonstrate the effectiveness of the our main theorems. Furthermore, we present and illustrate an example which does not satisfy the assumptions of our theorem and whose solution demonstrates nonoscillatory behavior.

Suggested Citation

  • Jehad Alzabut & James Viji & Velu Muthulakshmi & Weerawat Sudsutad, 2020. "Oscillatory Behavior of a Type of Generalized Proportional Fractional Differential Equations with Forcing and Damping Terms," Mathematics, MDPI, vol. 8(6), pages 1-18, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:1037-:d:376076
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/6/1037/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/6/1037/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jehad Alzabut & Weerawat Sudsutad & Zeynep Kayar & Hamid Baghani, 2019. "A New Gronwall–Bellman Inequality in Frame of Generalized Proportional Fractional Derivative," Mathematics, MDPI, vol. 7(8), pages 1-15, August.
    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. Weerawat Sudsutad & Nantapat Jarasthitikulchai & Chatthai Thaiprayoon & Jutarat Kongson & Jehad Alzabut, 2022. "Novel Generalized Proportional Fractional Integral Inequalities on Probabilistic Random Variables and Their Applications," Mathematics, MDPI, vol. 10(4), pages 1-21, February.

    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:8:y:2020:i:6:p:1037-:d:376076. 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.