Common fixed point theorem in bipolar controlled b-dislocated metric space and its application to some nonlinear equations

The existence and uniqueness of common fixed point theorems are demonstrated in this work through the use of [Formula: see text]-cyclic [Formula: see text]-contraction mapping and bipolar controlled b-dislocated metric space. In the scope of an application, we consider the potential for a unique common solution for nonintegral and nonlinear fractional differential equations.