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

Abstract

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.

B‐almost periodic solutions in finite‐dimensional distributions for octonion‐valued stochastic shunting inhibitory cellular neural networks

“…Based on the above discussions, and considering that time delay is universal, and in a certain sense, -almost periodic oscillation is the most complex almost periodic oscillation [42][43][44], the main purpose of this paper is to study the existence of -almost periodic solutions in finite-dimensional distributions for the following octonion-valued stochastic shunting inhibitory cellular neural network with time delays:…”

Anti-periodic Solutions Dynamics for Fractional-order Inertia Cohen-Grossberg Neural Networks

“…Fractional calculus is a generalization of integral calculus [1,2]. Many scholars have obtained important results on the dynamic behavior of fractional-order neural networks in the past few years, such as the stochastic stability of fractional competitive neural networks [3], Mittag-Leffler stability of fractional-order pulse control neural networks [4], almost periodic solutions of fractional-order quaternion numerical neural networks [5,6]and antiperiodic solutions of fractional BAM neural networks [7], etc. It is worth noting that scholars have begun to study fractional-order neural networks with inertial terms in recent years.…”

Multi-dimensional Besicovitch almost periodic type functions and applications

“…For further information about Besicovitch almost periodic functions, Besicovitch almost automorphic functions and their applications, we refer the reader to [1,2,4,5,6,7,9,11,12], [13,14,15,16,29,31,32,35], [36,49,51,53,54,56,57,58,60] and references cited therein; we would like to specially emphasize here the important research monograph [55] by A. A. Pankov.…”