A parametrized approach to generalized fractional integral inequalities: Hermite-Hadamard and Maclaurin variants

Lakhdari A., Bin-Mohsin B., Jarad F., Xu H., Meftah B.

JOURNAL OF KING SAUD UNIVERSITY SCIENCE, vol.36, no.11, 2024 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 11
  • Publication Date: 2024
  • Doi Number: 10.1016/j.jksus.2024.103523
  • Journal Name: JOURNAL OF KING SAUD UNIVERSITY SCIENCE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, BIOSIS, zbMATH, Directory of Open Access Journals
  • Kocaeli University Affiliated: No

Abstract

This paper introduces a novel parametrized integral identity that forms the basis for deriving a comprehensive class of generalized fractional integral inequalities. Building on recent advancements in fractional calculus, particularly in conformable fractional integrals, our approach offers a unified framework for various known inequalities. The novelty of this work lies in its ability to generate new and more general inequalities, including Hermite-Hadamard-, Maclaurin-, and corrected Maclaurin-type inequalities, by selecting specific parameter values. These results extend the scope of fractional integral inequalities and provide new insights into their structure. To demonstrate the practical applicability and accuracy of the theoretical findings, we present a detailed numerical example along with graphical representations.