Generalized AB-Fractional Operator Inclusions of Hermite–Hadamard’s Type via Fractional Integration

Abstract

The aim of this research is to explore fractional integral inequalities that involve interval-valued preinvex functions. Initially, a new set of fractional operators is introduced that uses the extended generalized Mittag-Leffler function Eμ,α,lγ,δ,k,c(τ;p) as a kernel in the interval domain. Additionally, a new form of Atangana–Baleanu operator is defined using the same kernel, which unifies multiple existing integral operators. By varying the parameters in Eμ,α,lγ,δ,k,c(τ;p), several new fractional operators are obtained. This study then utilizes the generalized AB integral operators and the preinvex interval-valued property of functions to establish new Hermite–Hadamard, Pachapatte, and Hermite–Hadamard–Fejer inequalities. The results are supported by numerical examples, graphical illustrations, and special cases.

Keywords

• Hermite–Hadamard inequality
• pachpatte inequality
• Mittag-Leffler
• fractional integrals
• preinvex function
• Fejer