New Generalized the Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals

Abstract

In this paper, a new identity for the generalized fractional integral is defined, through which new integral inequality for functions whose first derivatives in absolute value are convex. The new generalized Hermite-Hadamard inequality for generalized convex function on fractal sets involving Katugampola type fractional integral is established. We derive trapezoid and mid-point type inequalities connected to these generalized Hermite-Hadamard inequality.

A Systematic Review on Hermite-Hadamard Inequality: Theory and Applications

“…Almutair and Kiliçman [4] extended Lemma 6 and Theorem 27 for Katugampola fractional integrals as follows.…”

“…Therefore, the H-H type inequalities, by which many results are studied, play important roles in the theory of convex functions. The convexities, along with many types of their generalizations, can be applied in different fields of sciences [70,4], through which many generalizations of H-H inequality for a variant types of convexities have been studied. Other extensions of H-H inequality include the formulation of problems related to fractional calculus, a branch of calculus dealing with derivatives and integrals of non-integer order [32, 24,5].…”