Existence And Stability Of Solutions For Initial Value Problems Of Fuzzy Evolution Equations With Time Delay

Evolution equations with delay is used to describe a class of development system that depends on both the current state and the past state,the characteristic of such kind of equations is to take into account the influence of the history on the current status of the system.In recent years,delay evolution equations are widely used in physics,engineering,chemistry,aerodynamics and other fields.However,due to the errors caused by observation,experiment and maintenance,the variables and parameters obtained are usually fuzzy,incomplete information,but not accurate.These uncertain factors are introduced into the time delay evolution equation,which is called the time-delay fuzzy evolution equation.At present,due to the wide application of evolution equations and fuzzy differential equations in various fields,the initial value problem of time-delay fuzzy evolution equations and its related theories have attracted the attention of many scholars.In view of this,this thesis systematically studies the existence and stability of two kinds of mild solutions of initial value problem for fuzzy evolution equations with time delay by using nonlinear analysis method.The full text is divided into three chapters,the details are as follows:In the first chapter,we study the existence and uniqueness of two kinds of mild solutions for the initial value problems of fuzzy evolution equations with delay in the generalized Hukuhara differentiable framework.Firstly,by using the contraction mapping principle,the existence and uniqueness of two kinds of mild solutions for first order fuzzy evolution equations with time delay are obtained.Secondly,the equivalent integral equation of the initial value problem of fractional fuzzy evolution equation is obtained by using fuzzy Laplace transform.On this basis,the existence and uniqueness of two kinds of mild solutions of the problem are obtained by using the principle of power contraction mapping,and the restriction of Lipschitz conditional coefficients of nonlinear function is completely removed.In the second chapter,Under the generalized Hukuhara differentiable framework,the existence and uniqueness of two kinds of mild solutions for the initial value problem of fuzzy evolution equations with delay is obtained by using the upper and lower solution method and monotone iterative technique.In the third chapter,the stability of two types of mild solutions and the continuous dependence of solutions on the initial value of the delay fuzzy development equation(1)are discussed under the generalized Hukuhara differentiability framework.