Numerical and Graphical Validations of Hermite-Hadamard, Fejér and Pachpatte-Type Integral Inequalities Pertaining to Interval Analysis

Abstract

Fractional inequalities and interval analysis are interdependent mathematical fields that have received much interest in recent years. Both concepts have a lot of applications in the field of applied sciences such as physics, signal processing, mathematical modeling, control theory, numerical analysis, uncertainty quantification, engineering and optimization problems. In this article, we present a new concept between two intervals related to center-radius ordered relations. First, we introduce the new definition, namely, interval-valued center-radius order generalized preinvex function. Further, we establish the novel perspective of the Hermite-Hadamard type inequality via a newly investigated concept pertaining to the Riemann-Liouville fractional integral operator in the frame of interval analysis. In addition, fractional Fejér type inequality of the first and second kind is also investigated via a newly introduced concept. Finally, we establish the fractional Pachpatte-type inequality in the frame of interval analysis. The graphical, numerical, and literature validity of the presented inequalities are also estimated. Some special instances of our general results are also stated in the form of corollaries and remarks. The present research provides an improved understanding of integral inequalities with fractional integral operators.