Finite-Approximate Controllability of <mml:semantics>ν</mml:semantics>-Caputo Fractional Systems

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Awadalla M., Mahmudov N. I., Alahmadi J.

FRACTAL AND FRACTIONAL, vol.8, no.1, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 8 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.3390/fractalfract8010021
  • Journal Name: FRACTAL AND FRACTIONAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, Directory of Open Access Journals
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

This paper introduces a methodology for examining finite-approximate controllability in Hilbert spaces for linear/semilinear nu-Caputo fractional evolution equations. A novel criterion for achieving finite-approximate controllability in linear nu-Caputo fractional evolution equations is established, utilizing resolvent-like operators. Additionally, we identify a control strategy that not only satisfies the approximative controllability property but also ensures exact finite-dimensional controllability. Leveraging the approximative controllability of the corresponding linear nu-Caputo fractional evolution system, we establish sufficient conditions for achieving finite-approximative controllability in the semilinear nu-Caputo fractional evolution equation. These findings extend and build upon recent advancements in this field. The paper also explores applications to nu-Caputo fractional heat equations.