HERMITE–HADAMARD-TYPE INEQUALITIES VIA MULTIPLICATIVE FRACTIONAL CALCULUS AND APPLICATIONS TO SUPERQUADRATIC STRUCTURES

This work presents new Hermite–Hadamard-type fractional integral inequalities formulated through multiplicative fractional operators characterized by a power-law kernel. It broadens the scope of the classical [Formula: see text] inequalities by establishing fractional variants that address both the product and quotient of multiplicatively superquadratic and subquadratic functions. The inclusion of superquadratic functions, recognized for their enhanced convexity-like nature, yields tighter bounds and more precise inequalities, offering significant potential for applications in optimization, information theory, and allied areas. By incorporating multiplicative fractional operators with a power-law kernel, the study introduces a nonlinear fractional framework that strengthens analytical methodologies for examining complex and dynamic systems. The validity of the theoretical outcomes is demonstrated through graphical representations. Furthermore, the investigation extends to applications involving special functions, moments of random variables and special means leading to the development of novel fractional recurrence relations within the framework of multiplicative calculus. Overall, these results not only expand and refine the well-known inequalities reported in the literature but also open new avenues for future research in both theoretical development and practical modeling contexts.