Qualitative study of a fixed point for a feedback control problem of Caputo-via Riemann-Liouville fractional order differential equation

Abstract

In this research, we investigate the qualitative study of a fixed point for a feedback control problem of Caputo-Via Riemann-Liouville fractional order differential equation, in two classes L₁(I) and C(I) in a bounded interval I = [0,T]. The main tool applied in this work is the technique Schauder fixed point Theorem. In both cases we present a sufficient conditions for a unique solution and the continuous dependence on some functions. Additionally, we delve into the study of Hyers-Ulam stability. Finally, some examples are provided to verify our investigation.