A Study on Existence and Controllability of Conformable Impulsive Equations

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Mahmudov N. I., Akgun G.

AXIOMS, vol.12, no.8, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12 Issue: 8
  • Publication Date: 2023
  • Doi Number: 10.3390/axioms12080787
  • Journal Name: AXIOMS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Azerbaijan State University of Economics (UNEC) Affiliated: No

Abstract

We study the existence/uniqueness of conformable fractional type impulsive nonlinear systems as well as the controllability of linear/semilinear conformable fractional type impulsive controlled systems. Using the conformable fractional derivative approach, we introduce the conformable controllability operator and the conformable controllability Gramian matrix in order to obtain the necessary and sufficient conditions for the complete controllability of linear impulsive conformable systems. We present a set of sufficient conditions for the controllability of the conformable semilinear impulsive systems.