The Averaging Of Some Kinds Of Set Differential Equations And Inclusions

As a generalization of ordinary differential equations,set-valued differential systems have important applications in physics,biology,medicine,astronomy and other fields.However it lacks the method of finding exact solution,the averaging has been developed in this system as an effective approximate analysis method.In this paper,we study the averaging of some kinds of set-valued differential equations and differential inclusions.By replacing a function by it's average,the differential system is simplified so that the corresponding average system is obtained,and the approximate relationship between the solutions of the two systems is studied.The main contents of the paper are as follows:1.Two kinds of the set-valued differential equations involving causal operators with memory are studied,the full averaging theorem and the partial averaging theorem are given respectively.2.In this paper,the impulsive fuzzy differential equations with delay is studied,first,the full averaging is given,and then the application of the averaging is discussed when the average of the right-hand side function is absent.3.In this paper,the averaging of impulsive differential inclusions with supremum is studied.By giving the integral equation which is equivalent to the differential inclusion,the asymptotic relation between the original differential inclusions and the average differential inclusions is studied.