in this manuscript,we depict the concept of composed operators and then establish the existence and uniqueness of coupled coincidence points of such contractions and other related mappings in the abstract framework of multiplicative cone metric space over Banach algebra with multiplicative algebra solid cone regardless of its normality property. Further, we give illustrative examples to demonstrate the validity of our results proved herein, Eventually, we introduce an application of non-linear integral equations for the existence of a unique solution to support our results. In doing so, we show that some prvious results are consequences of our main presentd results.