Lipschitz Stability in Time for Riemann–Liouville Fractional Differential Equations

Abstract

A system of nonlinear fractional differential equations with the Riemann–Liouville fractional derivative is considered. Lipschitz stability in time for the studied equations is defined and studied. This stability is connected with the singularity of the Riemann–Liouville fractional derivative at the initial point. Two types of derivatives of Lyapunov functions among the studied fractional equations are applied to obtain sufficient conditions for the defined stability property. Some examples illustrate the results.

Keywords

• Riemann–Liouville fractional derivative
• differential equations
• Lipschitz stability in time