New Versions of Midpoint Inequalities Based on Extended Riemann-Liouville Fractional Integrals

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

FRACTAL AND FRACTIONAL, vol.7, no.6, 2023 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 6
  • Publication Date: 2023
  • Doi Number: 10.3390/fractalfract7060442
  • 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 prove some midpoint-type inequalities for fractional extended Riemann-Liouville integrals. Crucial equality is proven to build new results. Using this equality, several midpoint-type inequalities are established via differentiable convex functions and the proposed extended fractional operators. To be more specific, the well-known Holder, Jensen, and power mean integral inequalities are employed in the demonstrated inequalities. Additionally, many remarks based on specific selections of the main results are presented. Moreover, to illustrate the key conclusions, a few instances are provided.