Besicovitch Almost Periodic Solutions For Two Kinds Of Differential Equations

In this paper,the Besicovitch almost periodic solutions for two kinds of differential equations are mainly studied.Similar to the two definitions of Bohr almost periodic function,we give the definition of Besicovitch almost periodic function by using Bohr property and the limit function of uniform convergence of trigonometric polynomial sequence respectively,and study some basic properties for two kinds of Besicovitch almost periodic functions,especially the composition theorem,the equivalence of Bohr definition and Bochner definition of Besicovitch almost periodic functions.As applications,the existence of Besicovitch almost periodic solutions for a class of fractional-order quaternionvalued neural networks with discrete and infinitely distributed delays and the existence of Besicovitch almost periodic solutions for a class of semilinear functional differential equations are studied based on the fixed point theorem.In addition,the finite time stability of Besicovitch almost periodic solutions for fractional-order neural networks is obtained by using the generalized gronwall inequality and two numerical examples are utilized to show the fesibility of the obtained results.