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On Fractal–Fractional Simpson-Type Inequalities: New Insights and Refinements of Classical Results

Author

Listed:
  • Fahad Alsharari

    (Department of Mathematics, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia)

  • Raouf Fakhfakh

    (Department of Mathematics, College of Science, Jouf University, Sakaka P.O. Box 2014, Saudi Arabia)

  • Abdelghani Lakhdari

    (Laboratory of Energy Systems Technology, National Higher School of Technology and Engineering, Annaba 23005, Algeria)

Abstract

In this paper, we introduce a novel fractal–fractional identity, from which we derive new Simpson-type inequalities for functions whose first-order local fractional derivative exhibits generalized s -convexity in the second sense. This work introduces an approach that uses the first-order local fractional derivative, enabling the treatment of functions with lower regularity requirements compared to earlier studies. Additionally, we present two distinct methodological frameworks, one of which achieves greater precision by refining classical outcomes in the existing literature. The paper concludes with several practical applications that demonstrate the utility of our results.

Suggested Citation

  • Fahad Alsharari & Raouf Fakhfakh & Abdelghani Lakhdari, 2024. "On Fractal–Fractional Simpson-Type Inequalities: New Insights and Refinements of Classical Results," Mathematics, MDPI, vol. 12(24), pages 1-26, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:24:p:3886-:d:1540590
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    References listed on IDEAS

    as
    1. Huixia Mo & Xin Sui, 2014. "Generalized -Convex Functions on Fractal Sets," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, July.
    2. Yunxiu Zhou & Tingsong Du, 2023. "THE SIMPSON-TYPE INTEGRAL INEQUALITIES INVOLVING TWICE LOCAL FRACTIONAL DIFFERENTIABLE GENERALIZED (s,P)-CONVEXITY AND THEIR APPLICATIONS," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(05), pages 1-32.
    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).
    4. Yu, Yuping & Liu, Jun & Du, Tingsong, 2022. "Certain error bounds on the parameterized integral inequalities in the sense of fractal sets," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    5. Butt, Saad Ihsan & Khan, Ahmad, 2023. "New fractal–fractional parametric inequalities with applications," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    6. Hongyan Xu & Abdelghani Lakhdari & Wedad Saleh & Badreddine Meftah, 2024. "Some New Parametrized Inequalities On Fractal Set," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(03), pages 1-14.
    Full references (including those not matched with items on IDEAS)

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