Coupled fixed points of nonlinear operators with applications

It is a well known fact that contraction conditions play a major role in composing coincidence point results. In present work, a new $\varphi$-contraction is being corroborated to yield coupled coincidence points in partially ordered GV-fuzzy metric spaces. Due to the significant feature of H-type t-norm, in this communication, we endue GV-fuzzy metric spaces with this t-norm. We use the mixed monotone property of mappings with regard to partial ordering. Present work generalizes some already existing results. An applied example is also formulated to cast the 3-dimensional analysis of $\varphi$-contraction utilized in the main result. Computational analysis of the illustrative example has been done using the software MATLAB version R2022b which shows the experimental verification of our work. Furthermore, applications to the solution of the system of Fredholm type integral equations and solution of the system of equations in dynamic programming accords the validity of the present work. Endmost, the concluding remark projects the significance of current work.