Fixed Point Theorems for Multi-Valued Contractions in $b$ -Metric Spaces With Applications to Fractional Differential and Integral Equations

Muhammad Shoaib,Fahd Jarad,Thabet Abdeljawad,Muhammad Sarwar

doi:10.1109/access.2019.2938635

Abstract

The aim of this manuscript is to establish common fixed points results for multi-valued mappings via generalized rational type contractions in complete b-metric spaces. Using the derived results, existence of solutions to certain integral equations and fractional differential equations in the frame of Caputo fractional derivative are studied. Examples are provided for the authenticity of the presented work.

Highlights

AND PRELIMINARIESFractional calculus has been given proper attention in the last few decades by researchers
Remark1: The author in [36] proved common fixed points for single valued mapping in metric spaces while in Theorem 2.1 we proved common fixed points for multivalued mapping in b-metric space
Remark2: The author in [22] proved periodic points for single valued mapping while in Theorem 2.3 we proved common fixed points for multi-valued mapping in b-metric space

Summary

Introduction

AND PRELIMINARIESFractional calculus has been given proper attention in the last few decades by researchers. Chen and Sun [11] established fixed points for the (ψ, φ) weaker contractive mappings in generalized complete metric spaces. M. Shoaib et al.: Fixed Point Theorems for Multi-Valued Contractions in b-Metric Spaces

Results

Conclusion