Existence of Common Fixed point for $b$-Metric Rational Type Contraction

The necessary conditions for existence of a common fixed point of two mappings satisfying generalized $b$-order contractive condition in the setting of a partially ordered $b$-complete $b$-metric space are presented. Also, we study well-posedness of common fixed point problem for generalized $b$-order contractive mappings. We employ our result to establish an existence of a solution of an integral equation.