One new theorem for Caputo fractional derivative and two new theorems for Caputo fractional order systems,when 1 < a < 2,are proposed in this paper.The results have proved to be useful in order to apply the frac...One new theorem for Caputo fractional derivative and two new theorems for Caputo fractional order systems,when 1 < a < 2,are proposed in this paper.The results have proved to be useful in order to apply the fractional-order extension of Lyapunov direct method,to demonstrate the instability and the stability of many fractional order systems,which can be nonlinear and time varying.展开更多
This paper presents Lyapunov-type inequalities for fractional differential systems with more than three monomials by using the Gronwall-Inequality and the Greens function.The results of this paper extend the research ...This paper presents Lyapunov-type inequalities for fractional differential systems with more than three monomials by using the Gronwall-Inequality and the Greens function.The results of this paper extend the research methods of similar problems and generalize some early conclusions on this topic.In addition,with the help of the results,we can analyze the solution of differential systems.展开更多
基金Supported by the Natural Science Foundation of China(11661065)Youth Fundation of Pingxiang University
文摘One new theorem for Caputo fractional derivative and two new theorems for Caputo fractional order systems,when 1 < a < 2,are proposed in this paper.The results have proved to be useful in order to apply the fractional-order extension of Lyapunov direct method,to demonstrate the instability and the stability of many fractional order systems,which can be nonlinear and time varying.
基金Supported by the Natural Science Foundation of China(11661065) the Scientific Research Foundation of Jiangxi Provincial Education Department(GJJ161265)
文摘This paper presents Lyapunov-type inequalities for fractional differential systems with more than three monomials by using the Gronwall-Inequality and the Greens function.The results of this paper extend the research methods of similar problems and generalize some early conclusions on this topic.In addition,with the help of the results,we can analyze the solution of differential systems.