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

Fahad Alsharari (), Raouf Fakhfakh and Abdelghani Lakhdari
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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

Mathematics, 2024, vol. 12, issue 24, 1-26

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.

Keywords: Simpson inequality; generalized s-convexity; generalized integrals; fractal sets (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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