This study investigates the existence of solutions for certain systems of integral equations in multi-component models with asymmetric and heterogeneous dynamics, using fixed point theory. Classical metric frameworks are not sufficiently flexible to adequately capture these systems, highlighting the need for more flexible approaches. To address these challenges, a Perov-type vector-valued metric space endowed with a triangle inequality controlled by two matrices is introduced, which extends classical metric frameworks by incorporating two independent control matrices. This double-controlled structure significantly enlarges the admissible class of mappings and allows component-wise control adapted to heterogeneous dynamics. Within this setting, the concept of M_-admissible pairs of selfmaps is defined, and new common fixed point theorems under generalized matrix-type contraction conditions are established, extending several existing results in the literature. The proposed methodology is applied to a two-dimensional integral equation system, and a numerical example is presented to validate the theoretical results.
Pari Amiri (Fri,) studied this question.