A New extension of Hermite Hadamard inequalities associating ψ-Hilfer fractional integral

Qayyum A., BUDAK H., Bat U., Kara H., Munir A., Rathour L.

Palestine Journal of Mathematics, vol.14, no.1, pp.578-586, 2025 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 1
  • Publication Date: 2025
  • Journal Name: Palestine Journal of Mathematics
  • Journal Indexes: Scopus
  • Page Numbers: pp.578-586
  • Keywords: Convexity, Hermite-Hadamard inequality, ψ-Hilfer fractional integral
  • Kocaeli University Affiliated: Yes

Abstract

Fractional inequalities have been an essential topic in mathematics and have found applications in various domains. In this article, we established some new bounds (below and above) for mid-point type inequality and trapezoidal-type inequality for ψ-Hilfer- fractional integral by utilizing functions whose second derivatives are bounded. We also investigate some new generalization and extension of Hermite-Hadamard type inequalities for ψ-Hilfer fractional integrals for the functions having the condition: (Formula presented).