This manuscript is dedicated to the existence and uniqueness of weighted pseudo almost automorphic solution of dynamic equation which models cellular neural network with time varying delay on time scales. The coefficients are assumed to be weighted Stepanov-like pseudo almost automorphic functions which is more general than weighted pseudo almost automorphic function. We present new result on composition theorem on time scales for the space of such functions which is important for working on nonlinear differential equations. Moreover, we obtain the exponential stability of solution using Halanay inequality. These obtained results improve and extend previous related work. Toward the last, an example with simulations for \(\mathbb {R}\) and \({\mathbb {Z}}\), which are two particular time scales, is given for the adequacy of the hypothetical outcomes.

中文翻译：

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具有权重Stepanov-like（$$ S ^ p $$ Sp）的时间尺度上动力方程的加权拟概自纯解的存在性和稳定性

该手稿致力于动力学方程的加权伪几乎自同解的存在和唯一性，该动力学方程在时标上具有时变时延，对细胞神经网络进行建模。假定系数是加权的类似于Stepanov的伪几乎自纯函数，比加权的伪几乎自纯函数更通用。我们在时间标度上针对此类函数的空间给出了关于合成定理的新结果，这对于研究非线性微分方程很重要。此外，我们使用Halanay不等式获得解的指数稳定性。这些获得的结果改进并扩展了先前的相关工作。最后，给出一个模拟\（\ mathbb {R} \）和\（{\ mathbb {Z}} \）的示例给出了两个特定的时间尺度，以确保假设结果的充分性。