New Estimates on Hermite-Hadamard Type Inequalities via Generalized Tempered Fractional Integrals for Convex Functions with Applications

This paper presents a novel approach by introducing a set of operators known as the left and right generalized tempered fractional integral operators. These operators are utilized to establish new Hermite-Hadamard inequalities for convex functions as well as the multiplication of two convex functions. Additionally, this paper gives two useful identities involving the generalized tempered fractional integral operator for differentiable functions. By leveraging these identities, our results consist of integral inequalities of the Hermite-Hadamard type, which are specifically designed to accommodate convex functions. Furthermore, this study encompasses the identification of several special cases and the recovery of specific known results through comprehensive research. Lastly, this paper offers a range of applications in areas such as matrices, modified Bessel functions and q-digamma functions.

Automated summary

This paper presents a novel approach using the left and right generalized tempered fractional integral operators to establish new Hermite-Hadamard inequalities and multiplication rules for convex functions. It also provides two useful identities involving the generalized tempered fractional integral operator for differentiable functions. The results include integral inequalities of the Hermite-Hadamard type specifically designed for convex functions, and the study covers the identification of special cases and recovery of known results through comprehensive research. Furthermore, this paper offers various applications in areas such as matrices, modified Bessel functions, and q-digamma functions.