The Global Existence And Asymptotic Behavior Of Solutions To Time Fractional Stochastic Delay Evolution Equations With Nonlinear Multiplicative Tempered Fractional Noise And Poisson White Noise

Time fractional stochastic delay evolution equation with nonlinear multiplicative tempered fractional noise and Poisson white noise can be widely used to simulate many phenomena in finance,economics,medicine,biology,engineering and other scientific fields,so it has a good research value.In this paper,we mainly study the global existence and asymptotic behavior of solutions of time fractional stochastic delay evolution equations with nonlinear multiplicative tempered fractional noises and Poisson white noises.This paper is divided into three parts.In the first part,we give some basic definitions of Poisson point process,tempered fractional Brownian motion and fractional Brownian motion,and some necessary preliminary knowledge.In this part,we prove two important lemmas,which play a key role in the later proof.In the second part,we prove the global existence and uniqueness of mild solutions by using semigroup methods,and give a relevant example.In the third part,we consider an equation which is different from the equation in the second part.In this part,we prove that the existence and uniqueness of the local solution by applying Banach fixed point theorem,then extend the local solution to the global solution.Furthermore,we consider the exponential stability of the solution in the mean square sense.