Some New Versions of Hermite–Hadamard Integral Inequalities in Fuzzy Fractional Calculus for Generalized Pre-Invex Functions via Fuzzy-Interval-Valued Settings
Muhammad Bilal Khan, Muhammad Aslam Noor, Nehad Ali Shah, Khadijah M. Abualnaja, Thongchai Botmart
Abstract
The purpose of this study is to prove the existence of fractional integral inclusions that are connected to the Hermite–Hadamard and Hermite–Hadamard–Fejér type inequalities for χ-pre-invex fuzzy-interval-valued functions. Some of the related fractional integral inequalities are also proved via Riemann–Liouville fractional integral operator, where integrands are fuzzy-interval-valued functions. To prove the validity of our main results, some of the nontrivial examples are also provided. As specific situations, our findings can provide a variety of new and well-known outcomes which can be viewed as applications of our main results. The results in this paper can be seen as refinements and improvements to previously published findings.