Controllability of impulsive fractional nonlinear control system with Mittag-Leffler kernel in Banach space

Document Type : Research Paper


Department of mathematics, College of Education for Pure Sciences, University of Babylon, Babel, Iraq


In this paper, we study the controllability of a nonlinear impulsive fractional control system with Mittag-Leffler kernel in Banach space. Firstly, we present the mild solution of the control system using fractional calculus and semigroup theory. We set sufficient conditions to prove the controllability of the control system using the Nussbaum fixed point theorem. Finally, to illustrate our results, an example is given.


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Volume 13, Issue 1
March 2022
Pages 3257-3280
  • Receive Date: 11 June 2021
  • Revise Date: 22 August 2021
  • Accept Date: 19 October 2021