51. On Controllability of Fractional Continuous-Time Systems
- Author
-
Mina Ghasemi and Kameleh Nassiri
- Subjects
Article Subject ,General Mathematics ,010102 general mathematics ,General Engineering ,Engineering (General). Civil engineering (General) ,01 natural sciences ,Fractional calculus ,Controllability ,Nonlinear system ,Schauder fixed point theorem ,0103 physical sciences ,QA1-939 ,Applied mathematics ,TA1-2040 ,0101 mathematics ,010306 general physics ,Mathematics - Abstract
The aim of this paper is to study the controllability of fractional systems involving the Atangana–Baleanu fractional derivative using the Caputo approach. In the first step, the solution of a linear fractional system is obtained. Then, based on the obtained solution, some necessary and sufficient conditions for the controllability of such a system will be presented. Afterwards, the controllability of a nonlinear fractional system will be analyzed, based on these results. Our tool for the presentation of the sufficient conditions of controllability in this part is Schauder fixed point theorem. In the last step, the analytical results are illustrated by numerical examples.
- Published
- 2021