Interval valued Hadamard-Fejér and Pachpatte Type inequalities pertaining to a new fractional integral operator with exponential kernel

Abstract

The aim of this research is to combine the concept of inequalities with fractional integral operators, which are the focus of attention due to their properties and frequency of usage. By using a novel fractional integral operator that has an exponential function in its kernel, we establish a new Hermite-Hadamard type integral inequality for an LR-convex interval-valued function. We also prove new fractional-order variants of the Fejér type inequalities and the Pachpatte type inequalities in the setting of pseudo-order relations. By showing several numerical examples, we further validate the accuracy of the results that we have derived in this study. We believe that the results, presented in this article are novel and that they will be beneficial in encouraging future research in this field.

Keywords

• lr-convex interval-valued function
• fractional integral operator
• hermite–hadamard type inequality
• pachpatte type inequality
• fejér type inequality
• exponential kernel