carpathian_2026_42_1_171-189Abstract.
Modern science is continually seeking new types of functions to meet industrial demands. These needs have expanded to include the analysis of brain activity and advancements in artificial intelligence, particularly in the realms of machine learning and deep learning. Our research is centered on this area of functional analysis.
This paper introduces advanced concepts known as operational almost periodic alpha unpredictable functions. To develop this idea, we present a new operational research method for analyzing qualitative dynamic features. In simple terms, this method effectively distinguishes between regularity and irregularity in the dynamics of chaotic processes. Specifically, we identify almost periodic and alpha unpredictable components within the solutions of linear and quasilinear differential equations. Together, these components produce a functional dependence that could significantly contribute to research on complexity in today’s challenging problems. The theoretical results are illustrated through both analytical and graphical representations of specific dynamics.
