TEMPERED FRACTIONAL HERMITE–HADAMARD-TYPE INEQUALITIES FOR s-CONVEX STOCHASTIC PROCESSES

This paper investigates Hermite–Hadamard-type inequalities for [Formula: see text]-convex stochastic processes using stochastic tempered fractional integrals. We work within a stochastic tempered fractional integral framework, interpreted either as a natural extension or adaptation of existing tempered operators to the stochastic setting, and establish a fundamental Hermite–Hadamard inequality for [Formula: see text]-convex stochastic processes. Two new integral identities involving stochastic tempered fractional operators are derived, serving as key tools for obtaining a series of midpoint- and trapezium-type inequalities. These inequalities hold under the assumption that the sample-path derivatives, in the mean-square sense, are [Formula: see text]-convex. Our results provide stochastic analogues of classical and fractional deterministic inequalities, offering new analytical estimates for random processes exhibiting tempered memory effects.