The (ψ,φ)-orthogonal interpolative contractions and an application to fractional differential equations

Abstract

In this manuscript, we introduce the (?,?)-orthogonal interpolative contraction as a generalization of an orthogonal interpolative contraction. We prove several fixed point theorems stating conditions under which (?,?)-orthogonal interpolative contraction admits a fixed point. Our fixed point results are improvements of several known results in literature. As an application, we resolve a fractional differential equation.