Common Fixed Point Theorems for Novel Admissible Contraction with Applications in Fractional and Ordinary Differential Equations

Abstract

In our work, we offer a novel idea of contractions, namely an (α,β,γ)P−contraction, to prove the existence of a coincidence point and a common fixed point in complete metric spaces. This leads us to an extension of previous results in the literature. Furthermore, we applied our acquired results to prove the existence of a solution for ordinary and fractional differential equations with integral-type boundary conditions.

Keywords

• Geraghty function
• admissibility
• contraction
• common fixed point