Separation and stability of solutions to nonlinear systems involving Caputo–Fabrizio derivatives

Abstract

Abstract This work mainly investigates the separation and stability of solutions to nonlinear systems involving Caputo–Fabrizio fractional derivatives. An inequality ensuring the positivity of the fractional derivative at a given point is derived, by which the sufficient conditions for the separation of solutions are obtained. The comparison principle and the inequality for the fractional derivatives of convex functions are obtained, by which the approach of the convex Lyapunov functions is extended effectively to establish the criteria for the stability of solutions in the context of Caputo–Fabrizio fractional derivatives. Applications of the main results are illustrated by using examples.

Keywords

• Caputo–Fabrizio derivatives
• Nonlinear systems
• Stability
• Separation of solutions
• Convex Lyapunov functions