(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In this paper, we establish the notion of controlled rectangular modular metric space as a generalization of modular b-metric space and rectangular b-metric space. We used contraction mappings to find the existence and uniqueness of a fixed point in the framework of controlled rectangular modular metric space. We give several non-trivial examples and show the validity of contraction mappings via graphs. At the end, we utilize our main result to solve a non-linear fractional differential equation.