Controllability of Nonlinear Fractional Dynamical Systems with a Mittag–Leffler Kernel

• Main Authors: Jiale Sheng, Wei Jiang, Denghao Pang, Sen Wang
• Format: Article
• Language: English
• Published: MDPI AG 2020-12-01
• Series: Mathematics
• Subjects: controllability; Mittag–Leffler kernel; nonlinear; fixed point theorem
• Online Access: https://www.mdpi.com/2227-7390/8/12/2139

This paper is concerned with controllability of nonlinear fractional dynamical systems with a Mittag–Leffler kernel. First, the solution of fractional dynamical systems with a Mittag–Leffler kernel is given by Laplace transform. In addition, one necessary and sufficient condition for controllability of linear fractional dynamical systems with Mittag–Leffler kernel is established. On this basis, we obtain one sufficient condition to guarantee controllability of nonlinear fractional dynamical systems with a Mittag–Leffler kernel by fixed point theorem. Finally, an example is given to illustrate the applicability of our results.