Common Fixed Point Theorems for Generalized Contractive Pair of Mappings in a Metric Space and Their Application to Fractional Calculus

In this manuscript, we have established relation-theoretic version of some common fixed point results in metric space for generalized 
 
 β
 −
 ϕ
 −
 Z
 
 -contractive pair of mappings furnished with an arbitrary binary relation 
 
 R
 
 . Recently, the concept of binary relation is well known leading trend in fixed point theory. Our results extend and unify several fixed point theorems present in the literature. An illustrative example is given to support our main theorem. Finally, we exploit our main result for proving existence and uniqueness results to established the solution of a fractional differential equation of Caputo type.