Investigation of Fractional and Ordinary Differential Equations via Fixed Point Theory‎

Javad Hamzehnejadi, Rahmatollah Lashkaripour

Abstract

In this paper, we introduce the concept of generalized $\alpha$-$h$-$\phi$-contraction mapping and investigate the existence of the fixed point for such mappings in complete metric spaces. The presented results generalize many well known results in the literature. Moreover, we discuss the application of our results to the differential equations theory.