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

Abstract

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.