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Volume 8
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10.3390/math8122139
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Article

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

by
Jiale Sheng
1,*,
Wei Jiang
1,*,
Denghao Pang
2 and
Sen Wang
1
1
School of Mathematical Sciences, Anhui University, Hefei 230601, China
2
School of Internet, Anhui University, Hefei 230601, China
*
Authors to whom correspondence should be addressed.
Mathematics 2020, 8(12), 2139; https://doi.org/10.3390/math8122139
Submission received: 28 October 2020 / Revised: 26 November 2020 / Accepted: 26 November 2020 / Published: 1 December 2020
Versions Notes

Abstract

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.
Keywords: controllability; Mittag–Leffler kernel; nonlinear; fixed point theorem controllability; Mittag–Leffler kernel; nonlinear; fixed point theorem

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MDPI and ACS Style

Sheng, J.; Jiang, W.; Pang, D.; Wang, S. Controllability of Nonlinear Fractional Dynamical Systems with a Mittag–Leffler Kernel. Mathematics 2020, 8, 2139. https://doi.org/10.3390/math8122139

AMA Style

Sheng J, Jiang W, Pang D, Wang S. Controllability of Nonlinear Fractional Dynamical Systems with a Mittag–Leffler Kernel. Mathematics. 2020; 8(12):2139. https://doi.org/10.3390/math8122139

Chicago/Turabian Style

Sheng, Jiale, Wei Jiang, Denghao Pang, and Sen Wang. 2020. "Controllability of Nonlinear Fractional Dynamical Systems with a Mittag–Leffler Kernel" Mathematics 8, no. 12: 2139. https://doi.org/10.3390/math8122139

APA Style

Sheng, J., Jiang, W., Pang, D., & Wang, S. (2020). Controllability of Nonlinear Fractional Dynamical Systems with a Mittag–Leffler Kernel. Mathematics, 8(12), 2139. https://doi.org/10.3390/math8122139

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