Lyapunov-type inequalities for fractional quasilinear problems via variational methods
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Authors
Mohamed Jleli
- Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh, 11451, Saudi Arabia.
Mokhtar Kirane
- LaSIE, Pole Sciences et Technologies, Université de La Rochelle, Avenue M. Crépeau, 17042 La Rochelle Cedex, France.
Bessem Samet
- Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh, 11451, Saudi Arabia.
Abstract
In this paper, by variational methods, some Lyapunov-type inequalities are established for fractional quasilinear problems
involving left and right Riemann-Liouville fractional derivative operators. To the authors’ knowledge, this is the first work,
where Lyapunov-type inequalities for fractional boundary value problems are investigated by using variational methods. As an
application of the obtained inequalities, we extend the notion of generalized eigenvalues to a fractional quasilinear system, and
we derive some geometric properties of the fractional generalized spectrum.
Share and Cite
ISRP Style
Mohamed Jleli, Mokhtar Kirane, Bessem Samet, Lyapunov-type inequalities for fractional quasilinear problems via variational methods, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 5, 2471--2486
AMA Style
Jleli Mohamed, Kirane Mokhtar, Samet Bessem, Lyapunov-type inequalities for fractional quasilinear problems via variational methods. J. Nonlinear Sci. Appl. (2017); 10(5):2471--2486
Chicago/Turabian Style
Jleli, Mohamed, Kirane, Mokhtar, Samet, Bessem. "Lyapunov-type inequalities for fractional quasilinear problems via variational methods." Journal of Nonlinear Sciences and Applications, 10, no. 5 (2017): 2471--2486
Keywords
- Lyapunov inequality
- fractional derivative
- variational method
- fractional quasilinear system
- fractional generalized eigenvalues.
MSC
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