Numerical Interpretation and Graphical Visualization of Generalized Fuzzy Fractional Inequalities Through Different Convexities

The generalization of convexities and fractional operators is a significant approach that not only refines the fractional inequalities but has also resolved many problems that are facing the non-integer family of calculus. In this paper, we introduce the class of modified exponential–trigonometric functions, (p,s)-convex functions, and (s)-convex functions, and include them in a single framework of modified exponential trigonometric (p,s)-convex (MET-(p,s)-convex) functions. The present concept is generalized to the fuzzy-interval-valued case by means of Prabhakar fuzzy fractional integral operators. We obtain new Hermite–Hadamard- and trapezoid-type inequalities and their Hölder and power mean refinements. Lower and upper endpoint functions are utilized to prove the obtained results, and the results are also unified by fuzzy-order relation. The proposed class is a strict generalization of several convexity classes and fits some non-convex mappings not covered by the classical Hermite–Hadamard inequality. Moreover, the obtained inequalities offer computable upper and lower bounds to the uncertainty of Prabhakar fractional means. Theoretical results are illustrated by numerical examples and graphical illustrations, which show that the main advantage of the proposed framework is a wider class of admissible mappings rather than sharper numerical bounds. The classical Hermite–Hadamard inequality and several existing convexity-based inequalities are recovered as special cases of the results obtained here.