The stability and control of fractional nonlinear system with distributed time delay

In this paper, we study the stability of fractional nonlinear systems with distributed-delay under Caputo derivatives. We propose a novel stability theorem via establishing an extending item on the basis of the stability theorem of fractional nonlinear systems without delay, and prove the theorem by utilizing the function monotonous properties and the stability theorem of fractional linear system without delay. Analyzing and controlling some fractional nonlinear systems with distributed delay are taken as examples to illustrate the theorems. Numerical simulation results confirm the effectiveness of the proposed methods.