THE µ-NEUTRAL FRACTIONAL MULTI-DELAYED DIFFERENTIAL EQUATIONS

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Aydın M., Mahmudov N. I.

Miskolc Mathematical Notes, vol.25, no.1, pp.109-125, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 25 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.18514/mmn.2024.4208
  • Journal Name: Miskolc Mathematical Notes
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.109-125
  • Keywords: existence and uniqueness, linear differential equations, stability, µ-fractional derivative, µ-fractional neutral multi-delayed differential equation, µ-neutral multi-delay perturbation
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

The µ-neutral linear fractional multi-delayed differential nonhomogeneous system with noncommutative coefficient matrices is introduced. The novel µ-neutral multi-delayed perturbation of Mittag-Leffler type matrix function is proposed. Based on this, an explicit solution to the system is investigated step by step. The existence uniqueness of solutions to µ-neutral nonlinear fractional multi-delayed differential system is obtained with regard to the supremum norm. The notion of stability analysis in the sense of solutions to the described system is discussed on the grounds of the fixed point approach.