Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 11 3 2026 09 01 On Hermite-Hadamard Type Inequalities in Stochastic Fractional Calculus 1059 1071 15076 10.22049/cco.2025.30980.2689 EN Asraa Najm Abood Department of Mathematics, College of Dentistry, Diyala University, Diyala, Iraq Rawaa Khalil Ibrahim Department of Mathematics, College of Dentistry, University of Diyala, Diyala, Iraq Journal Article 2025 09 08 This paper extends Hermite-Hadamard type inequalities within the framework of stochastic fractional calculus. We investigate how fractional integrals, which account for memory effects, interact with random processes. Our work presents three main contributions. First, we provide an error bound for approximating a standard integral of a smooth, deterministic function using stochastic fractional integrals. Second, we extend the well-known Hermite-Hadamard inequality, which applies to convex functions, to the setting of convex stochastic processes, showing how their expected values are bounded by these integrals. Finally, we derive specific mean-square error bounds when approximating a standard Brownian motion using its stochastic fractional integrals. These results enhance our understanding of stochastic fractional inequalities, offering new tools for analyzing complex systems influenced by both memory and randomness. https://comb-opt.azaruniv.ac.ir/article_15076_d59e0a6111c47b0ff2c87c9134bf06e0.pdf