Fixed Point Theory in Metric Spaces | Original Article
Using fixed point theorems, the primary objective of this study is to provide existence results and stability conditions for a class of fractional order differential equations. Existence findings are derived from Schauder's fixed point theorem and the Banach contraction principle. In addition, the use of Krasnoselskii's fixed point theorem to develop stability conditions for a particular class of fractional order differential equations is given a lot of attention. The usefulness of the stability result is shown via the use of an example. Through using the characteristics of -distance mappings and -admissible mappings, we present the idea of generalized contraction mappings and show the existence of a fixed-point theorem for such mappings. This is accomplished by mapping properties. In addition, we extend our conclusion to the theorems of coincidence point and common fixed point in metric spaces. Further, the fixed-point theorems that are endowed with an arbitrary binary relation may also be deduced from our conclusions thanks to this line of reasoning.