Existence and stability analysis for a coupled system of $ \mathtt{q} $-fractional implicit jerk Caputo derivatives with $ \mathtt{q} $-Erdélyi-Kober fractional integral conditions

This manuscript demonstrates the existence, uniqueness, and different kinds of Ulam stability for a $ \mathtt{q} $-Caputo implicit fractional jerk coupled system involving $ \mathtt{q} $-fractional Erdélyi-Kober integral conditions. The existence and uniqueness results were investigated by employing the Leray-Schauder alternative and the Banach contraction mapping principle. We also derived various kinds of Ulam stability under specific conditions. We provided an example to verify our main results.