This paper investigates the maximal and minimal solutions of initial value problem for n-th order nonlinear integro-differential equations of Volterra type on an infinite interval in a Banach space by establishing a c...This paper investigates the maximal and minimal solutions of initial value problem for n-th order nonlinear integro-differential equations of Volterra type on an infinite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.展开更多
This paper investigates periodic boundary value problem for first order nonlinear impulsive integro-differelltial equations of mixed type in a Banach space. By establishing a comparison result, criteria on the existen...This paper investigates periodic boundary value problem for first order nonlinear impulsive integro-differelltial equations of mixed type in a Banach space. By establishing a comparison result, criteria on the existence of maximal and minimal solutions are obtained.展开更多
The state-space representation of linear time-invariant (LTI) fractional order systems is introduced, and a proof of their stability theory is also given. Then an efficient identification algorithm is proposed for tho...The state-space representation of linear time-invariant (LTI) fractional order systems is introduced, and a proof of their stability theory is also given. Then an efficient identification algorithm is proposed for those fractional order systems. The basic idea of the algorithm is to compute fractional derivatives and the filter simultaneously, i.e., the filtered fractional derivatives can be obtained by computing them in one step, and then system identification can be fulfilled by the least square method. The instrumental variable method is also used in the identification of fractional order systems. In this way, even if there is colored noise in the systems, the unbiased estimation of the parameters can still be obtained. Finally an example of identifying a viscoelastic system is given to show the effectiveness of the aforementioned method.展开更多
文摘This paper investigates the maximal and minimal solutions of initial value problem for n-th order nonlinear integro-differential equations of Volterra type on an infinite interval in a Banach space by establishing a comparison result and using the monotone iterative technique.
文摘This paper investigates periodic boundary value problem for first order nonlinear impulsive integro-differelltial equations of mixed type in a Banach space. By establishing a comparison result, criteria on the existence of maximal and minimal solutions are obtained.
文摘The state-space representation of linear time-invariant (LTI) fractional order systems is introduced, and a proof of their stability theory is also given. Then an efficient identification algorithm is proposed for those fractional order systems. The basic idea of the algorithm is to compute fractional derivatives and the filter simultaneously, i.e., the filtered fractional derivatives can be obtained by computing them in one step, and then system identification can be fulfilled by the least square method. The instrumental variable method is also used in the identification of fractional order systems. In this way, even if there is colored noise in the systems, the unbiased estimation of the parameters can still be obtained. Finally an example of identifying a viscoelastic system is given to show the effectiveness of the aforementioned method.
