In the present paper,with the help of the resolvent operator and some analytic methods,the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with ...In the present paper,with the help of the resolvent operator and some analytic methods,the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with state-dependent delay.As an application,we also give one example to demonstrate our results.展开更多
The functions of bounded φ-variation are development and generalization of bounded variation functions in the usual sense.Henstock-Kurzweil integral is a very useful tool for some discontinuous systems. In this paper...The functions of bounded φ-variation are development and generalization of bounded variation functions in the usual sense.Henstock-Kurzweil integral is a very useful tool for some discontinuous systems. In this paper, by using Henstock-Kurzweil integral, we establish theorems of continuous dependence of bounded D-variation solutions on parameter for a class of discontinuous systems on the base of D-function. These results are essential generalizations of continuous dependence of bounded variation solutions on parameter for the systems.展开更多
The basic objects of investigation in this article are nonlinear impulsive dif- ferential equations. The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-called barrier c...The basic objects of investigation in this article are nonlinear impulsive dif- ferential equations. The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-called barrier curves. For such type of equations, suf- ficient conditions are found under which the solutions are continuously dependent on the perturbations with respect to the initial conditions and barrier curves. The results are applied to a mathematical model of population dynamics.展开更多
文摘In the present paper,with the help of the resolvent operator and some analytic methods,the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with state-dependent delay.As an application,we also give one example to demonstrate our results.
基金Supported by the National Natural Science Foundation of China(10771171)Supported by the 555 Innovation Talent Project of Gansu Province(GS-555-CXRC)+1 种基金Supported by the Technique Innovation Project of Northwest Normal University(NWNU-KJCXGC-212)Supported by the Youth Foundation of Dingxi Advanced Teachers College(1333)
文摘The functions of bounded φ-variation are development and generalization of bounded variation functions in the usual sense.Henstock-Kurzweil integral is a very useful tool for some discontinuous systems. In this paper, by using Henstock-Kurzweil integral, we establish theorems of continuous dependence of bounded D-variation solutions on parameter for a class of discontinuous systems on the base of D-function. These results are essential generalizations of continuous dependence of bounded variation solutions on parameter for the systems.
文摘The basic objects of investigation in this article are nonlinear impulsive dif- ferential equations. The impulsive moments coincide with the moments of meeting of the integral curve and some of the so-called barrier curves. For such type of equations, suf- ficient conditions are found under which the solutions are continuously dependent on the perturbations with respect to the initial conditions and barrier curves. The results are applied to a mathematical model of population dynamics.
