In this paper, we are concerned with the solvability for a class of nonlinear sequential fractional dynamical systems with damping infinite dimensional spaces, which involves fractional Riemann-Liouville derivatives. ...In this paper, we are concerned with the solvability for a class of nonlinear sequential fractional dynamical systems with damping infinite dimensional spaces, which involves fractional Riemann-Liouville derivatives. The solutions of the dynamical systems are obtained by utilizing the method of Laplace transform technique and are based on the formula of the Laplace transform of the Mittag-Leffler function in two parameters. Next, we present the existence and uniqueness of solutions for nonlinear sequential fractional dynamical systems with damping by using fixed point theorems under some appropriate conditions.展开更多
In this study,we focus on the controllability of fractional-order damped systems in linear and nonlinear cases with multiple time-varying delays in control.For the linear system based on the Mittag-Leffler matrix func...In this study,we focus on the controllability of fractional-order damped systems in linear and nonlinear cases with multiple time-varying delays in control.For the linear system based on the Mittag-Leffler matrix function,we define a controllability Gramian matrix,which is useful in judging whether the system is controllable or not.Furthermore,in two special cases,we present serval equivalent controllable conditions which are easy to verify.For the nonlinear system,under the controllability of its corresponding linear system,we obtain a sufficient condition on the nonlinear term to ensure that the system is controllable.Finally,two examples are given to illustrate the theory.展开更多
文摘In this paper, we are concerned with the solvability for a class of nonlinear sequential fractional dynamical systems with damping infinite dimensional spaces, which involves fractional Riemann-Liouville derivatives. The solutions of the dynamical systems are obtained by utilizing the method of Laplace transform technique and are based on the formula of the Laplace transform of the Mittag-Leffler function in two parameters. Next, we present the existence and uniqueness of solutions for nonlinear sequential fractional dynamical systems with damping by using fixed point theorems under some appropriate conditions.
基金Project supported by the National Natural Science Foundation of China(No.61803386)the Natural Science Foundation of Shanghai,China(No.19ZR1400500)。
文摘In this study,we focus on the controllability of fractional-order damped systems in linear and nonlinear cases with multiple time-varying delays in control.For the linear system based on the Mittag-Leffler matrix function,we define a controllability Gramian matrix,which is useful in judging whether the system is controllable or not.Furthermore,in two special cases,we present serval equivalent controllable conditions which are easy to verify.For the nonlinear system,under the controllability of its corresponding linear system,we obtain a sufficient condition on the nonlinear term to ensure that the system is controllable.Finally,two examples are given to illustrate the theory.
