Well-Posedness And Regularity Of Solutions For Two-Dimensional Fractional Nonlocal Diffusion Stochastic Lattice Systems With Delays

Many natural physical phenomena cannot be described simply by integer derivative because of their complexity.Fractional derivative can be applied to a wider range of applications due to its unique memory characteristics.At the same time,stochastic interference is everywhere,and the introduction of stochastic term can more accurately reflect the problem we are studying.In this paper,we study a two-dimensional fractional nonlocal diffusion stochastic lattice system with delay on C([-h,0];Lp(?;lp))(p? 2)(fractional exponent ? ?[1/2,1)),and to prove the well-posedness and regularity of its solutions.First,we prove the existence and uniqueness of solutions of fractional nonlocal diffusion stochastic lattice system by using Banach fixed point theorem,and show that the solutions are global.The key is to use the properties of Mittag-Leffler function to prove the compressibility of the operator S?,to exert BurkholderDavis-Gundy inequality to deal with the stochastic term of fractional nonlocal diffusion stochastic lattice system and overcome the difficulties of two-dimensional nonlocal diffusion lattice system and delay term.We then use a similar method to prove the continuous dependence on initial values and the fractional exponent a of solutions of two-dimensional fractional nonlocal diffusion stochastic system.Finally,we analyze the regularity of solutions about time.It is worth noting that this paper studies the two-dimensional nonlocal diffusion stochastic lattice system of fractional exponential ??(1/2,1).The range of fractional exponential is limited by the research method in this paper.It is hoped that this limitation can be broken through in the subsequent research process,and to study the two-dimensional nonlocal diffusion stochastic lattice system of fractional exponential ? ?(0,1).