Controllability and Ulam–Hyers stability of fractional order linear systems with variable coefficients

Abstract

In this paper we study the Controllability and the generalized Ulam-Hyers stability of Riemann-Liouville fractional order linear differential equations with variable coefficients in Banach spaces. We obtained the desired results by means of fixed point principle and fractional calculus. Furthermore, we used the Gronwall’s inequality to investigate above type of stability for Riemann-Liouville fractional order linear differential equation with time dependent coefficients under some specific assumptions. An example is also provided at the end to illustrate the theoretical work.

Keywords

• Riemann–Liouville integral
• Caputo derivative
• Impulse
• Ulam–Hyers stability
• Banach contraction