New Multiplicative Fractional Integral Inequalities

Abstract

In the context of multiplicative fractional calculus, we develop new Hermite-Hadamard (HH) type inequalities and present the concept of multiplicative trigonometric exponen- tial convex (MTEC) functions. We investigate their algebraic properties and show how these functions relate to other types of convex functions. Several new fractional HH type inequalities are constructed by employing product and quotient of newly introduced multi- plicative convexities via multiplicative Riemann-Liouville (RL) integrals operator. Further, we derive some fractional auxiliary results of trapezoid and midpoint type and apply our convexities to formulate new bounds. In addition, we also verify the validity of our results by graphical descriptions. We also strengthen our study by providing some applications to special functions.