On Conformable Fractional Milne-Type Inequalities

Ying R., Lakhdari A., Xu H., Saleh W., Meftah B.

SYMMETRY-BASEL, vol.16, no.2, 2024 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 2
  • Publication Date: 2024
  • Doi Number: 10.3390/sym16020196
  • Journal Name: SYMMETRY-BASEL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Kocaeli University Affiliated: No

Abstract

Building upon previous research in conformable fractional calculus, this study introduces a novel identity. Using this identity as a foundation, we derive a set of conformable fractional Milne-type inequalities specifically designed for differentiable convex functions. The obtained results recover some existing inequalities in the literature by fixing some parameters. These novel contributions aim to enrich the analytical tools available for studying convex functions within the realm of conformable fractional calculus. The derived inequalities reflect an inherent symmetry characteristic of the Milne formula, further illustrating the balanced and harmonious mathematical structure within these frameworks. We provide a thorough example with graphical representations to support our findings, offering both numerical insights and visual confirmation of the established inequalities.