Positive Solutions of q-Fractional Boundary Value Problems with Two Parameters

In this research, we investigate the uniqueness results of fractional \(\textsf{q}\) -differential equations under certain specified integral boundary conditions. We utilize the properties of using the \(\upgamma\) -concave and sub-homogeneous operators, along with a Banach fixed-point theorem, to achieve our results. Additionally, an example is provided to illustrate the main results. This work contributes to the field by examining the existence and uniqueness of positive solutions involving new integral boundary conditions with the \(\upgamma\) -concave and sub-homogeneous operators, leading to illustrative numerical results.