Computational Illustration of Fractional Inequalities via 2D Graphs with Application

Abstract

In this article, we use generalized $(k, s)$-Riemann-Liouville fractional integral operator (GRLFIO) to explore the reverse forms of Minkowskis, Holder and Hermite-Hadamard-Fejer type inequalities within an interval-valued $(\imath.\upsilon)$ $(\leftthreetimes^{s+1},\mho)$ class of convexity. We comprise various existing definitions and propose the novel concept of an $\imath.\upsilon$ $(\leftthreetimes^{s+1},\mho)$ convexity. Our findings show the remarkable adaptability by adjusting parameter bounds for $(k, s)$-GRLFIO within structure of an $\imath.\upsilon$ $(\leftthreetimes^{s+1},\mho)$ convexity presenting broader generalization and new perspective  advancements to Hermite-Hadamard-Fejer and Pachpatte-type inequalities. In order to facilitate their applications, we examine the further consequences, constructed specific inequalities and illustrate them through graphical representations.  Additionally, we validate the results using tables for various fractional orders. This study establishes the foundation for future research into the mathematical inequalities by emphasizing the importance of fractional integral operators and the expanded concept of convexity.