Nonlinear Mittag-Leffler stability of nonlinear fractional partial differential equations
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Authors
Ibtisam Kamil Hanan
- Institute of Engineering Mathematics, Universiti Malaysia Perlis, Pauh Putra Main Campus, 02600 Arau, Perlis, Malaysia.
- Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, P. O. Box 47077, Baghdad, Iraq.
Muhammad Zaini Ahmad
- Institute of Engineering Mathematics, Universiti Malaysia Perlis, Pauh Putra Main Campus, 02600 Arau, Perlis, Malaysia.
Fadhel Subhi Fadhel
- Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, P. O. Box 47077, Baghdad, Iraq.
Abstract
This paper focuses on the application of fractional backstepping control scheme for nonlinear fractional partial differential equation (FPDE). Two types of fractional derivatives are considered in this paper, Caputo and the Grünwald-Letnikov fractional derivatives. Therefore, obtaining highly accurate approximations for this derivative is of a great
importance. Here, the discretized approach for the space variable is used to transform the FPDE into a system of fractional differential equations. The convergence of the closed loop system is guaranteed in the sense of Mittag-Leffler stability. An illustrative example is given to demonstrate the effectiveness of the proposed control scheme.
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ISRP Style
Ibtisam Kamil Hanan, Muhammad Zaini Ahmad, Fadhel Subhi Fadhel, Nonlinear Mittag-Leffler stability of nonlinear fractional partial differential equations, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 10, 5182--5200
AMA Style
Hanan Ibtisam Kamil, Ahmad Muhammad Zaini, Fadhel Fadhel Subhi, Nonlinear Mittag-Leffler stability of nonlinear fractional partial differential equations. J. Nonlinear Sci. Appl. (2017); 10(10):5182--5200
Chicago/Turabian Style
Hanan, Ibtisam Kamil, Ahmad, Muhammad Zaini, Fadhel, Fadhel Subhi. "Nonlinear Mittag-Leffler stability of nonlinear fractional partial differential equations." Journal of Nonlinear Sciences and Applications, 10, no. 10 (2017): 5182--5200
Keywords
- Backstepping method
- fractional Lyapunov function
- fractional derivative
- boundary control
- fractional partial differential equation
MSC
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