Besicovitch almost periodic solutions for fractional-order quaternion-valued neural networks with discrete and distributed delays

In this paper, we study a class of fractional-order quaternion-valued neural networks with discrete and distributed delays by direct method. We first investigate some properties of Besicovitch almost periodic functions, including the composition theorem with deviating arguments. Then, we obtain the existence and uniqueness of Besicovitch almost periodic solutions for such class of networks by considering an appropriate Banach space and using the contraction mapping principle. Furthermore, by making use of a generalized Gronwall inequality, we gain the finite-time stability of the Besicovitch almost periodic solution. Even if the network under consideration degenerates into a real-valued or complex-valued networks, the results of this paper are still brand new. Finally, we use a numerical example to show the feasibility of our theoretical results.