IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2022i1p146-d1017448.html
   My bibliography  Save this article

On Some Error Bounds for Milne’s Formula in Fractional Calculus

Author

Listed:
  • Muhammad Aamir Ali

    (Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China)

  • Zhiyue Zhang

    (Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China)

  • Michal Fečkan

    (Department of Mathematical Analysis and Numerical Mathematics, Comenius University in Bratislava, Mlynská dolina, 842 48 Bratislava, Slovakia
    Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73 Bratislava, Slovakia)

Abstract

In this paper, we found the error bounds for one of the open Newton–Cotes formulas, namely Milne’s formula for differentiable convex functions in the framework of fractional and classical calculus. We also give some mathematical examples to show that the newly established bounds are valid for Milne’s formula.

Suggested Citation

  • Muhammad Aamir Ali & Zhiyue Zhang & Michal Fečkan, 2022. "On Some Error Bounds for Milne’s Formula in Fractional Calculus," Mathematics, MDPI, vol. 11(1), pages 1-11, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:146-:d:1017448
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/1/146/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/1/146/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Emad A. Az-Zo’bi & Kamel Al-Khaled & Amer Darweesh, 2019. "Numeric-Analytic Solutions for Nonlinear Oscillators via the Modified Multi-Stage Decomposition Method," Mathematics, MDPI, vol. 7(6), pages 1-13, June.
    2. Muhammad Uzair Awan & Sadia Talib & Yu-Ming Chu & Muhammad Aslam Noor & Khalida Inayat Noor, 2020. "Some New Refinements of Hermite–Hadamard-Type Inequalities Involving - Riemann–Liouville Fractional Integrals and Applications," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-10, April.
    3. Du, Tingsong & Li, Yujiao & Yang, Zhiqiao, 2017. "A generalization of Simpson’s inequality via differentiable mapping using extended (s, m)-convex functions," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 358-369.
    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. Limei Dai & Xuewen Guo, 2022. "Parabolic Hessian Equations Outside a Cylinder," Mathematics, MDPI, vol. 10(16), pages 1-16, August.
    2. Luo, Chunyan & Wang, Hao & Du, Tingsong, 2020. "Fejér–Hermite–Hadamard type inequalities involving generalized h-convexity on fractal sets and their applications," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    3. Jorge E. Macías-Díaz, 2019. "Numerically Efficient Methods for Variational Fractional Wave Equations: An Explicit Four-Step Scheme," Mathematics, MDPI, vol. 7(11), pages 1-27, November.
    4. Huda J. Saeed & Ali Hasan Ali & Rayene Menzer & Ana Danca Poțclean & Himani Arora, 2023. "New Family of Multi-Step Iterative Methods Based on Homotopy Perturbation Technique for Solving Nonlinear Equations," Mathematics, MDPI, vol. 11(12), pages 1-13, June.
    5. Hüseyin Budak & Fatih Hezenci & Hasan Kara & Mehmet Zeki Sarikaya, 2023. "Bounds for the Error in Approximating a Fractional Integral by Simpson’s Rule," Mathematics, MDPI, vol. 11(10), pages 1-16, May.

    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:2022:i:1:p:146-:d:1017448. 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.