Hybrid Fixed Point Theorem with Applications to Forced Damped Oscillations and Infinite Systems of Fractional Order Differential Equations

Abstract

In this manuscript, hybrid common fixed point results in the setting of a $b$ -metric space are established. Our results generalized the results of Fisher, Khan, and Piri et al. for set-valued mapping in $b$ -metric spaces. Applications to forced damped oscillations, infinite systems of fractional order differential equations, and system of functional equations are also studied. We construct an example to support our main result.