Stability analysis of nonlinear fractional differential order systems with Caputo and Riemann--Liouville derivatives

Authors: JAVAD ALIDOUSTI, REZA KHOSHSIAR GHAZIANI, ALI BAYATI ESHKAFTAKI

Abstract: In this paper we establish stability theorems for nonlinear fractional orders systems (FDEs) with Caputo and Riemann--Liouville derivatives. In particular, we derive conditions for $ {\bf \cal{F}}$-stability of nonlinear FDEs. By numerical simulations, we verify numerically our theoretical results on a test example.

Keywords: Stability, Riemann--Liouville derivative, Caputo derivative, ${\bf \cal{F}}$-asymptotically stable,

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