Fractional Reverse Inequalities Involving Generic Interval-Valued Convex Functions and Applications

The relation between fractional calculus and convexity significantly impacts the development of the theory of integral inequalities. In this paper, we explore the reverse of Minkowski and Hölder’s inequality, unified Jensen’s inequality, and Hermite–Hadamard (H-H)-like inequalities using fractional calculus and a generic class of interval-valued convexity. We introduce the concept of I.V-(⋏,ℏ) generic class of convexity, which unifies several existing definitions of convexity. By utilizing Riemann–Liouville (R-L) fractional operators and I.V-(⋏,ℏ) convexity to derive new improvements of the H-H- and Fejer and Pachpatte-like inequalities. Our results are quite unified; by substituting the different values of parameters, we obtain a blend of new and existing inequalities. These results are fruitful for establishing bounds for I.V R-L integral operators. Furthermore, we discuss various implications of our findings, along with numerical examples and simulations to enhance the reliability of our results.