<p>We present some generalized Jensen type inequalities in measure theory for fractional integrals. Then we propose a new approach by introducing fractional Jensen’s gap in the model selection process. Our research shows that the models with smaller fractional Jensen’s gap are generally preferred in low-risk scenarios, as they demonstrate a closer alignment with investor risk aversion and provide more dependable outcomes in uncertain environments. In fact, by focusing on fractional Jensen’s gap, we are able to identify models that effectively minimize risk, thereby enhancing decision-making and improving overall model performance in real-world applications. Furthermore, by selecting appropriate kernels, we derive a comprehensive set of fractional Jensen gaps. Our results also refine the corresponding ones in the literature.</p>