A fixed point theorem for Hardy-Rogers type on generalized fractional differential equations

Abstract

In this research paper, we introduce a generalization of Hardy-Rogers type contraction in a metric like space. Moreover, we apply this technique to investigate the existence and uniqueness of solutions for the classical boundary value problems and generalized fractional boundary value problems through deducing the main properties of the related Green functions. The main result of this paper is to establish the modified conditions of Hardy-Roger's fixed point theorem and introduce some advanced applications.