Solvability of Multidimensional Integral Inclusion Systems via a Common Fixed Point Approach for 𝕄α-Admissible Multivalued Operators

Integral inclusion systems play a significant role in applied analysis and modeling, providing an effective framework for studying various physical, engineering, and dynamical processes. In this work, the solvability of a multidimensional integral inclusion system is investigated by applying the common fixed point technique to a pair of Mα-admissible multivalued operators. The analysis is carried out within a novel double-controlled vector-valued metric structure, in which the distance is governed by two independent matrix-valued control operators; this setting strictly extends classical Perov-type and b-metric frameworks and offers a more flexible tool for treating multidimensional and interdependent systems. Existence results are derived under a suitable contractive condition within a generalized metric structure. Several auxiliary theorems are established to support the main conclusions. To illustrate the applicability of the theoretical findings, the obtained results are utilized to ensure the existence of solutions for a multidimensional Urysohn-type integral inclusion system. A simple example demonstrates the validity of the theoretical framework and highlights the effectiveness of the adopted approach.