Inequalities of Simpson-Mercer-type including Atangana-Baleanu fractional operators and their applications

Abstract

Fractional operators with integral inequalities have attracted the interest of several mathematicians. Fractional inequalities are best utilized in mathematical science with their features and wide range of applications in optimization, modeling, engineering and artificial intelligence. In this article, we consider new variants of Simpson-Mercer type inequalities involving the Atangana-Baleanu (A-B) fractional integral operator for s-convex functions. First, an integral identity, which acts as an auxiliary result for the main results is proved in the frame of fractional operator. Employing this new identity, some estimations of Simpson-Mercer type for s-convex functions in the second sense are discussed. In addition, we study various new applications on Modified Bessel functions, special means and q-digamma functions. These applications confirm the effectiveness and validity of the results and also bring a different dimension to the study.

Keywords

• jensen-mercer inequality
• simpson's inequality
• s-convex functions
• atangana-baleanu fractional operator
• hölder's inequalities
• q-digamma functions
• modified bessel functions