Fixed Point Theory in Metric Spaces

Existence and Stability Results in Fixed Point Theory

Abstract

Using fixed point theorems, the primary objective of this study is to provide existence resultsand stability conditions for a class of fractional order differential equations. Existence findings are derivedfrom Schauder's fixed point theorem and the Banach contraction principle. In addition, the use ofKrasnoselskii's fixed point theorem to develop stability conditions for a particular class of fractional orderdifferential equations is given a lot of attention. The usefulness of the stability result is shown via the useof an example. Through using the characteristics of -distance mappings and -admissible mappings, wepresent the idea of generalized contraction mappings and show the existence of a fixed-point theorem forsuch mappings. This is accomplished by mapping properties. In addition, we extend our conclusion tothe theorems of coincidence point and common fixed point in metric spaces. Further, the fixed-pointtheorems that are endowed with an arbitrary binary relation may also be deduced from our conclusionsthanks to this line of reasoning.