IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0311386.html
   My bibliography  Save this article

On Riemann-Liouville integrals and Caputo Fractional derivatives via strongly modified (p, h)-convex functions

Author

Listed:
  • Ammara Nosheen
  • Khuram Ali Khan
  • Mudassir Hussain Bukhari
  • Michael Kikomba Kahungu
  • A F Aljohani

Abstract

The paper introduces a new class of convexity named strongly modified (p, h)-convex functions and establishes various properties of these functions, providing a comprehensive understanding of their behavior and characteristics. Additionally, the paper investigates Schur inequality and Hermite-Hadamard (H-H) inequalities for this new class of convexity. Also, H-H inequalities are proved within context of Riemann-Liouville integrals and Caputo Fractional derivatives. The efficiency and feasibility of Schur inequality and H-H inequalities are supported by incorporating multiple illustrations, that demonstrate the applicability of strongly modified (p, h)-convex functions. The results contribute to the field of mathematical analysis and provide valuable insights into the properties and applications of strongly modified (p, h)-convex functions.

Suggested Citation

  • Ammara Nosheen & Khuram Ali Khan & Mudassir Hussain Bukhari & Michael Kikomba Kahungu & A F Aljohani, 2024. "On Riemann-Liouville integrals and Caputo Fractional derivatives via strongly modified (p, h)-convex functions," PLOS ONE, Public Library of Science, vol. 19(10), pages 1-18, October.
    • Handle: RePEc:plo:pone00:0311386
    DOI: 10.1371/journal.pone.0311386
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0311386
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0311386&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0311386?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
    ---><---

    References listed on IDEAS

    as
    1. Muhammad Shoaib Saleem & Yu-Ming Chu & Nazia Jahangir & Huma Akhtar & Chahn Yong Jung & Ming-Sheng Liu, 2020. "On Generalized Strongly p-Convex Functions of Higher Order," Journal of Mathematics, Hindawi, vol. 2020, pages 1-8, September.
    2. Saad Ihsan Butt & Saba Yousaf & Muhammad Younas & Hijaz Ahmad & Shao-Wen Yao, 2022. "Fractal Hadamard–Mercer-Type Inequalities With Applications," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(02), pages 1-14, March.
    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. Butt, Saad Ihsan & Khan, Ahmad, 2023. "New fractal–fractional parametric inequalities with applications," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    2. Du, Tingsong & Yuan, Xiaoman, 2023. "On the parameterized fractal integral inequalities and related applications," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    3. Yu, Shuhong & Zhou, Yunxiu & Du, Tingsong, 2022. "Certain midpoint-type integral inequalities involving twice differentiable generalized convex mappings and applications in fractal domain," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

    More about this item

    Statistics

    Access and download statistics

    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:plo:pone00:0311386. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.