In the first part of this work, we start by introducing the generalized pseudo almost periodic and automorphic functions in time space scales. The concept in the Bohr, Bochner, Weyl, Stepanov, and Besicovitch sense will be explained. By the Banach’s fixed point theorem and constructing the adequate Lyapunov functionals, we fixed sufficient criteria that guarantee the existence, uniqueness, convergence, and stability of various dynamical neural networks models. In addition, some numerical examples and simulations are performed to verify our theoretical results. The second part of this work is focused on the utility of neural networks for solving some mathematical problems as example : solving differential equations and optimization problems.