Stochastic processes are very important in statistics and probability, where finding upper and lower bounds of mean-square stochastic integral has led to a basic problem. In this paper we show that for mean-square differentiable stochastic process, the convexity condition in previous well-known results can be replaced by weaker conditions.

This paper presents new bounds for the left and right fractional mean-square stochastic integrals based on convex stochastic processes. Then a range is proposed that includes a linear combination of the left and right fractional mean-square stochastic integrals. Finally, the previous results presented in this subject are improved.