Solutions Of A Class Of Stochastic Evolution Equations With Fractional Derivatives

Let H be a Hilbert space and E a Banach space.In this paper,we set up a theory about the stochastic integration,which is about the integration of L(H,E)-valued functions,the functions is related to an H-cylindrical Liouville fractional Brownian motion,let?represent the Hurst parameter of an H-cylindrical Liouville fractional Brownian motion,where?has a value range of0<?<1.Further,for0<?<1/2 we show that a function?:(0,T)?L(H,E)is stochastically integrable with respect to an H-cylindrical Liouville fractional Brownian motion if and only if it is stochastically integrable with respect to an H-cylindrical fractional Brownian motion.Then,we study a class of stochastic evolution equations driven by H-cylindrical Liouville fractional Brownian motion,that is dU(t)=AU(t)dt+BdW_H~?(t) and we can prove the existence,uniqueness and space-time regularity of mild solutions on the Banach space E under the assumption of?with different values,in which has operators A:?(A)?E and B:H?E,the Hurst parameter is?.Finally,the above results are applied to a class of second-order parabolic stochastic partial differential equations driven by space-time noise,and it is proved that there exists a mild solution for the problem when d/4<?<1.