On Controllability of Impulsive Fractional Integro-differential Nonlocal System with State

Naseif J.  Al-Jawari; Abdul Khaleq O.  Mazeel; Khudair O.  Hussain

doi:10.24996/ijs.2022.63.5.26

Authors

Naseif J. Al-Jawari Department of Mathematics, College of Science, AL-Mustansiriyah University, Baghdad, Iraq
Abdul Khaleq O. Mazeel Department of Mathematics, College of Science, AL-Mustansiriyah University, Baghdad, Iraq
Khudair O. Hussain Department of Mathematics, College of Science, AL-Mustansiriyah University, Baghdad, Iraq https://orcid.org/0000-0001-7592-9699

DOI:

https://doi.org/10.24996/ijs.2022.63.5.26

Keywords:

Controllability, State-dependent delay, Semigroup theory, Probability density function, Krasnoselskii fixed point theorem

Abstract

This paper is concerned with the controllability of a nonlinear impulsive fractional integro-differential nonlocal control system with state-dependent delay in a Banach space. At first, we introduce a mild solution for the control system by using fractional calculus and probability density function. Under sufficient conditions, the results are obtained by means of semigroup theory and the Krasnoselskii fixed point theorem. Finally, an example is given to illustrate the main results.