Tempered fractional nonlocal lattice systems in Orlicz spaces with general growth and mixed delays

Under the guidelines of probability intuitions and stochastic perspectives of tempered Lévy flights, a class of tempered fractional nonlocal lattice systems is introduced for the first time which can be regarded as the generalized form of tempered fractional p-Laplacian system. Correspondingly, some property of discrete Orlicz spaces is established. Based on this framework, we first show the global existence of solutions for the lattice system via an existence theorem of solutions for an infinite system of ordinary differential equations. Besides, the existence and uniqueness of a D-pullback attractor {A(τ)}τ∈R is proved under general continuity assumptions and growth conditions but without Lipschitz hypothesis. The main idea is to show the pullback asymptotically upper semicompactness by deriving tails estimates of solutions and continuous dependence of solutions with respect to the initial data. There has not been published any work on the long-time behavior of tempered fractional nonlocal lattice systems with mixed delays, and this paper is devoted to fill this gap.