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

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 E-mu,alpha,l(gamma,delta, k,c) (tau; 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 E-mu,alpha,l(gamma,delta, k,c)(tau; 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.

Automated summary

The aim of this research is to explore fractional integral inequalities involving interval-valued preconvex functions. A new set of fractional operators is introduced using the extended generalized Mittag-Leffler function as a kernel in the interval domain. Furthermore, a new form of Atangana-Baleanu operator is defined using the same kernel, unifying multiple existing integral operators. New Hermite-Hadamard, Pachapatte, and Hermite-Hadamard-Fejer inequalities are established utilizing the generalized AB integral operators and the preconvex interval-valued property of functions.