Milne-Type inequalities via expanded fractional operators: A comparative study with different types of functions

Hyder A., Budak H., Barakat M. A.

AIMS MATHEMATICS, vol.9, no.5, pp.11228-11246, 2024 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 5
  • Publication Date: 2024
  • Doi Number: 10.3934/math.2024551
  • Journal Name: AIMS MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Page Numbers: pp.11228-11246
  • Kocaeli University Affiliated: No

Abstract

This study focused on deriving Milne-type inequalities using expanded fractional integral operators. We began by establishing a key equality associated with these operators. Using this equality, we explored Milne-type inequalities for functions with convex derivatives, supported by an illustrative example for clarity. Additionally, we investigated Milne-type inequalities for bounded and Lipschitzian functions utilizing fractional expanded integrals. Finally, we extended our exploration to Milne-type inequalities involving functions of bounded variation.