Generalized Fractional Integral Inequalities Derived from Convexity Properties of Twice-Differentiable Functions

Almoneef A. A., Hyder A., Hezenci F., Budak H.

FRACTAL AND FRACTIONAL, vol.9, no.2, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 2
  • Publication Date: 2025
  • Doi Number: 10.3390/fractalfract9020097
  • 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 presents novel formulations of fractional integral inequalities, formulated using generalized fractional integral operators and the exploration of convexity properties. A key identity is established for twice-differentiable functions with the absolute value of their second derivative being convex. Using this identity, several generalized fractional Hermite-Hadamard-type inequalities are developed. These inequalities extend the classical midpoint and trapezoidal-type inequalities, while offering new perspectives through convexity properties. Also, some special cases align with known results, and an illustrative example, accompanied by a graphical representation, is provided to demonstrate the practical relevance of the results. Moreover, the findings may offer potential applications in numerical integration, optimization, and fractional differential equations, illustrating their relevance to various areas of mathematical analysis.