A two-dimensional stochastic fractional non-local diffusion lattice model with delays

The well-posedness, regularity and general stability of solutions to a two-dimensional stochastic non-local delay diffusion lattice system with a time Caputo fractional operator of order alpha is an element of (1/2, 1) are investigated in Lp spaces for p >= 2. First, the global existence and uniqueness of solutions are established by using a temporally weighted norm, the Burkholder-Davis-Gundy inequality and the Banach fixed point theorem. Then the continuous dependence of solutions on initial values is established in the sense of pth moment. In particular, the pth moment Ho spexpressioncing diexpressioneresis lder regularities in time and pth moment general stability, including polynomial and logarithmic stability of solutions, are obtained.