Superquadratic stochastic processes and their fractional perspective with applications in information theory

Superquadraticity is a generalization of convexity that yields more refined results compared to those obtained through convexity alone. In this work, we established, for the first time, a class of superquadratic stochastic processes and explored their fundamental properties. Based on these properties, we derived Jensen's and (Hermite-Hadamard) $ \mathbb{HH} $'s type inequalities, along with their fractional counterparts, in the context of mean-square stochastic (Riemann-Liouville) $ \mathbb{R.L} $ fractional integrals. The validity of our findings was supported by graphical illustrations using suitable examples. Furthermore, we extended the applicability of our results to information theory by introducing several stochastic divergence measures.