Results on Minkowski-Type Inequalities for Weighted Fractional Integral Operators

Abstract

This article considers a general family of weighted fractional integral operators and utilizes this general operator to establish numerous reverse Minkowski inequalities. When it comes to understanding and investigating convexity and inequality, symmetry is crucial. It provides insightful explanations, clearer explanations, and useful methods to help with the learning of key mathematical ideas. The kernel of the general family of weighted fractional integral operators is related to a wide variety of extensions and generalizations of the Mittag-Leffler function and the Hurwitz-Lerch zeta function. It delves into the applications of fractional-order integral and derivative operators in mathematical and engineering sciences. Furthermore, this article derives specific cases for selected functions and presents various applications to illustrate the obtained results. Additionally, novel applications involving the Digamma function are introduced.

Keywords

• weighted fractional integral operators
• reverse Minkowski integral inequality
• digamma (or <i>ψ</i>-) function
• Mittag-Leffler functions
• Hurwitz-Lerch zeta function