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

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.