Fixed Point Theorems in Controlled Rectangular Modular Metric Spaces with Solution of Fractional Differential Equations

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.