New Generalized 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. Using this identity we studied a 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. This fractional integral generalizes Riemann-Liouville and Hadamard’s integral, which possess a symmetric property. We derive trapezoid and mid-point type inequalities connected to this generalized Hermite-Hadamard inequality.

The Necessary and Sufficient Optimality Conditions for a System of FOCPs with Caputo–Katugampola Derivatives

“…New types of fractional operators were introduced by U. Katugampola, These are done by generalizing the Riemann-Liouville and Hadamard FIs 17 and generalizing the Riemann-Liouville and Hadamard FDs 18 and new generalizations of fractional derivatives can also be seen in 19,20 . This paper aims to study and derive the necessary and sufficient optimality conditions for a new system of FOCPs subjected to the dynamic control system from integer and Caputo-Katugampola FDs in the form:…”

Generalized Fejér-Hermite-Hadamard type via generalized $(h-m)$-convexity on fractal sets and applications

“…Due to the enormous importance of inequalities ( 1) and ( 2), many generalizations of such inequalities involving a variant types of convexities have been investigated [13,19,15,17]. For more interesting results, one can consult the following references [20,14,9,18,5].…”