Fixed Point Theorems in Controlled Rectangular Modular Metric Spaceswith Solution of Fractional Differential Equations (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.
Keywords: modular metric space; existence and uniqueness; non-linear fractional differential equations; Controlled metric space