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In this chapter, using almost automorphic functions, we study the solutions of the integro-differential equations with reflection, which are of pseudo almost automorphic ( \(\mathscr {P}\mathscr {A}\mathscr {A}\) ) type, by introducing the Mittag-Lefler function. In the sequel, using the general measure theory and considering the Mittag-Leffler function, we first obtain the existence of a unique solution for the cellular neural equations and then investigate the stability of the Mittag-Leffler and the attractiveness of the Mittag-Leffler for pseudo almost periodic functions. Considering fuzzy measure theory and matrix-valued fuzzy norm spaces, we study a differential system of non-autonomous cellular neural networks with mixed delays (NA-CNN-MD).

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Cellular Neural Networks, Pseudo Almost Automorphic Solution

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  • 发表日期：

    2025年

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  • Zahra Eidinejad,
  • Reza Saadati,
  • Tofigh Allahviranloo,
  • Chenkuan Li,
  • Javad Vahidi

摘要

In this chapter, using almost automorphic functions, we study the solutions of the integro-differential equations with reflection, which are of pseudo almost automorphic ( \(\mathscr {P}\mathscr {A}\mathscr {A}\) ) type, by introducing the Mittag-Lefler function. In the sequel, using the general measure theory and considering the Mittag-Leffler function, we first obtain the existence of a unique solution for the cellular neural equations and then investigate the stability of the Mittag-Leffler and the attractiveness of the Mittag-Leffler for pseudo almost periodic functions. Considering fuzzy measure theory and matrix-valued fuzzy norm spaces, we study a differential system of non-autonomous cellular neural networks with mixed delays (NA-CNN-MD).