Existence And Uniqueness Of Solution For Two Kinds Of Fractional Lattice System And Exponential Attractor Of Fitzhugh-nagumo Lattice System

In recent years, fractional diferential equations and lattice system become a hot is-sue because of its wide range of applications in practice. This dissertation discusses thequestions about the existence and uniqueness of solutions for the fractional FitzHugh-Nagumo lattice system of infinite dimension and the fractional partially dissipationsystem of infinite dimension. Besides, we give the existence of exponential attractor ofFitzHugh-Nagumo lattice system of infinite dimension. This dissertation includes thefollowing two parts, the first part contains the second and third chapters. In the secondchapter, we consider the FitzHugh-Nagumo lattice system of infinite dimension withRiemann-Liouville fractional derivative. The global existence and uniqueness of itssolution is proved. In the third chapter, we consider partially dissipative lattice systemof infinite dimension with Riemann-Liouville fractional derivative. The local existenceand uniqueness of its solution is also proved. The second part contains the fourth chap-ter. we consider the FitzHugh-Nagumo lattice system of infinite dimension and provethe existence of its exponential attractor.