New Study of Prabhakar Operators Associated with Inequalities and its Significant Applications with Different Convexity (European Journal of Pure and Applied Mathematics, 2025)
Convexity plays a dominant role in the modification of fractional inequalities. Most fractional inequalities are proved based on different types of convexity and fractional operators, which have immense applications in various areas of mathematics. This article aims to investigate the Hermite-Hadamard type inequalities with a different kind of convexity by the implementation of Prabhakar fractional operators. Moreover, we discuss the behavior of trapezoidal type inequalities for the $h$-Godunova-Levin pre-invex function through Prabhakar fractional operators. Additionally, we present a comparison of our findings with existing literature, which are summarized through corollaries.
Keywords: Convexity; Hermite-Hadamard inequalities; trapezoid inequalities; Prabhaker fractional operators