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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
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    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)

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