In this paper, we consider the approximation of functions by sublinear positive operators with applications to several Max-Product operators under generalized fractional differentiability. Our study is based on our generalized fractional results about positive sublinear operators. We derive Jackson type inequalities under iterated initial conditions. So our approach is quantitative by producing inequalities with their right hand sides involving the modulus of continuity of generalized fractional derivative of the function under approximation.