In this paper, we presented the IDP-core with continuous updating in the cooperative differential games. Employing undominated IDP and time consistent as basic axioms within the context of continuous updating, we constructed a comprehensive definition of the IDP-core for continuous updating and developed a mathematical method to computation. Furthermore, we demonstrated the validity of our approach through rigorous proof. Our findings contributed significantly to advancing the understanding and application of cooperative solutions in differential games with continuous updating scenarios. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.