Modification of Inequalities by Prabhakar Fuzzy Fractional Operators along with its Applications

Abstract

The rapid advancement of fractional calculus has driven an increased demand for fractional operators and special functions. There exists a strong connection between special functions and fractional calculus, which facilitates the development of more generalized versions of fractional operators. These generalized operators are instrumental in solving numerous problems across applied, pure, and computational mathematics. Special functions play a crucial role in enhancing the extension and generalization of fractional operators. In this research, we explore various classes of convexity and generalized fractional operators, such as Prabhakar fractional operators, establishing their relationships with other fractional operators. Additionally, we investigate the fractional behavior of generalized inequalities through the application of fractional operators. Our study extends the Hermite-Hadamard inequality and its refinements involving differentiable convexity, deriving significant inequalities that reinforce the core objectives of our work.