Finite-time Stability Of Several Types Of Fractional-order Stochastic Differential Equation

This dissertation mainly studies the existence,uniqueness and finite-time stability of solutions for several classes of fractional stochastic differential equations.With the help of the Laplace transformation and its inverse,and using the contraction mapping principle,Picard iteration,and contradiction method,we prove the existence and uniqueness of the solutions for the considered system.In addition,by applying the properties of norm and the generalized Gr¨onwall inequality,we derive the finite-time stability results of the corresponding systems.The details are as follows:Firstly,with the aid of Laplace transformation and its inverse,and by utilizing the contraction mapping principle and the properties of norm,we deduce the existence,uniqueness and finite-time stability of the solutions for a class of -Hilfer fractional stochastic differential equations.Secondly,by using the contraction mapping principle and the generalized Gr¨onwall inequality,we establish the existence,uniqueness and finite-time stability of the solutions for a class of delay fractional stochastic differential equations.Thirdly,by using Picard iteration,contradiction method and the generalized Gr¨onwall inequality,we study the existence,uniqueness and finite-time stability of the solutions for a class of impulsive fractional stochastic differential equations.Subsequently,we also use the Laplace transformation and its inverse to derive the expression of solutions for a class of impulsive fractional stochastic differential equations,and then use the contraction mapping principle and properties of norm to establish the existence,uniqueness and finite-time stability of the solutions.In addition,corresponding examples are given to expound the theoretical results.