Extension of Hermite-Hadamard type inequalities to Katugampola fractional integrals

Abstract

In this study, we introduce several new Hermite-Hadamard type general integral inequalities for exponentially (s,m)-convex functions via Katugampola fractional integral. The Katugampola fractional integral is a broader form of the Riemann–Liouville and Hadamard fractional integrals. We utilized the power mean integral inequality, the H¨older inequality and a few additional generalizations to derive these inequalities. Numerous limiting results are derived from the main results presented in the remarks. Furthermore, we provide an example illustrating our theoretical findings, supported by a graphical representation.