B_ap~2-Almost Periodic Solution And Almost Automorphic Solution Of Two Kinds Of Quarternion-valued Differential Equations

In this paper,we study the existence and global exponential stability of Bap2-almost periodic solutions for quaternion-valued cellular neural networks with D operator,and the existence and Mittag-Leffler stability of almost automorphic solutions for fractional-order quaternion-valued fuzzy cellular neural networks with time delays.For the former,we first give the definition of Bap2-almost periodic function in Bohr's sense in equivalent class space M/L,and prove its related properties.Then we consider a class of quaternionvalued cellular neural networks with D operator,and obtain sufficient conditions for the existence of Bap2-almost periodic solutions of the system by using Banach fixed point theorem?Finally,we use the contradiction method to prove that the solution has global exponential stability.For the latter,we first study the existence of almost automorphic solutions of the fractional-order fuzzy neural network,and then prove that the almost automorphic solutions of the system are Mittag-Leffler stable by constructing appropriate Lyapunov functions and inequality techniques.Numerical examples are given in both parts of this paper to demonstrate the rationality and feasibility of the conclusions.