Operational almost periodic alpha unpredictability

AKHMET M., Zhamanshin A.

Carpathian Journal of Mathematics, vol.42, no.1, pp.171-189, 2026 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 1
  • Publication Date: 2026
  • Doi Number: 10.37193/cjm.2026.01.12
  • Journal Name: Carpathian Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.171-189
  • Keywords: Alpha unpredictable functions, Compartmental almost periodic alpha unpredictable functions, Degree of periodicity, Kappa property, Method of included intervals, Operational almost periodic alpha unpredictable functions, Quasilinear differential equations, Ultra Poincaré chaos
  • Middle East Technical University Affiliated: Yes

Abstract

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.