INTEGER AND FRACTIONAL ORDER INEQUALITIES OF m-SUPERQUADRATIC FUNCTION WITH APPLICATIONS

In this paper, we introduce the concept of m-superquadraticity, a natural generalization of classical superquadraticity that incorporates a parameter m to provide adjustable control over the growth and curvature of functions. Utilizing this framework, we establish new forms of Jensen's and (Hermite-Hadamard) HH type inequalities and extend them to their fractional counterparts via (Riemann-Liouville) R.L fractional integrals. The parameter m allows the inequalities to flexibly adapt to a wider class of functions, offering tighter bounds and greater applicability in analytical and applied contexts. The theoretical findings are substantiated with graphical illustrations and tabular analyses from representative examples. Furthermore, the m-superquadratic framework is applied in information theory to formulate novel classes of divergence measures. Overall, this approach enhances the classical theory of superquadraticity by providing additional flexibility, precision, and avenues for applications in stochastic fractional modeling, optimization under uncertainty, and entropy-based information measures.