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The existence and uniqueness of solutions for partially dissipative lattice system of infinite dimension

In the past decade, the fractional differential equation (FDE) model has been widely used in the fields of materials science[1], electrical engineering[2], control theory[3], signal processing[4], chaos[5], etc. As a result, the research of FDE solution has become a focus of many current studies. This study devotes itself to the solution of a fractional-order partially dissipative lattice system. The paper proves firstly that the operator T(Sr) is uniformly bounded, and then that it is equally continuous before finally proves, by applying the Schauder fixed point theorem, the existence and uniqueness of the solution of the fractional partial dissipative system.