Some New Fractal Milne-Type Integral Inequalities via Generalized Convexity with Applications

Meftah B., Lakhdari A., Saleh W., Kilicman A.

FRACTAL AND FRACTIONAL, vol.7, no.2, 2023 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.3390/fractalfract7020166
  • Journal Name: FRACTAL AND FRACTIONAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, Directory of Open Access Journals
  • Kocaeli University Affiliated: No

Abstract

This study aims to construct some new Milne-type integral inequalities for functions whose modulus of the local fractional derivatives is convex on the fractal set. To that end, we develop a novel generalized integral identity involving first-order generalized derivatives. Finally, as applications, some error estimates for the Milne-type quadrature formula and new inequalities for the generalized arithmetic and p-Logarithmic means are derived. This paper's findings represent a significant improvement over previously published results. The paper's ideas and formidable tools may inspire and motivate further research in this worthy and fascinating field.