IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i5p1133-d1079375.html
   My bibliography  Save this article

Analytical Contribution to a Cubic Functional Integral Equation with Feedback Control on the Real Half Axis

Author

Listed:
  • Ahmed M. A. El-Sayed

    (Faculty of Science, Alexandria University, Alexandria 21544, Egypt)

  • Hind H. G. Hashem

    (Faculty of Science, Alexandria University, Alexandria 21544, Egypt)

  • Shorouk M. Al-Issa

    (Faculty of Arts and Sciences, Department of Mathematics, The International University of Beirut, Beirut 1107, Lebanon
    Faculty of Arts and Sciences, Department of Mathematics, Lebanese International University, Saida 1600, Lebanon)

Abstract

Synthetic biology involves trying to create new approaches using design-based approaches. A controller is a biological system intended to regulate the performance of other biological processes. The design of such controllers can be based on the results of control theory, including strategies. Integrated feedback control is central to regulation, sensory adaptation, and long-term effects. In this work, we present a study of a cubic functional integral equation with a general and new constraint that may help in investigating some real problems. We discuss the existence of solutions for an equation that involves a control variable in the class of bounded continuous functions BC ( R + ) , by applying the technique of measure of noncompactness on R + . Furthermore, we establish sufficient conditions for the continuous dependence of the state function on the control variable. Finally, some remarks and discussion are presented to demonstrate our results.

Suggested Citation

  • Ahmed M. A. El-Sayed & Hind H. G. Hashem & Shorouk M. Al-Issa, 2023. "Analytical Contribution to a Cubic Functional Integral Equation with Feedback Control on the Real Half Axis," Mathematics, MDPI, vol. 11(5), pages 1-18, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1133-:d:1079375
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/5/1133/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/5/1133/
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Ahmed M. A. El-Sayed & Malak M. S. Ba-Ali & Eman M. A. Hamdallah, 2023. "Asymptotic Stability and Dependency of a Class of Hybrid Functional Integral Equations," Mathematics, MDPI, vol. 11(18), pages 1-18, September.

    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:11:y:2023:i:5:p:1133-:d:1079375. 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: 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.