A Lyapunov-type inequality for a fractional q-difference boundary value problem
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Authors
Mohamed Jleli
- Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia.
Bessem Samet
- Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia.
Abstract
In this paper, we establish a Lyapunov-type inequality for a fractional q-difference equation subject to
Dirichlet-type boundary conditions. The obtained inequality generalizes several existing results from the
literature including the standard Lyapunov inequality. We use that result to provide an interval, where
a certain Mittag-Leffler function has no real zeros. We present also another application of the obtained
inequality, where we prove that existence implies uniqueness for a certain class of fractional q-difference
boundary value problems.
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ISRP Style
Mohamed Jleli, Bessem Samet, A Lyapunov-type inequality for a fractional q-difference boundary value problem, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 5, 1965--1976
AMA Style
Jleli Mohamed, Samet Bessem, A Lyapunov-type inequality for a fractional q-difference boundary value problem. J. Nonlinear Sci. Appl. (2016); 9(5):1965--1976
Chicago/Turabian Style
Jleli, Mohamed, Samet, Bessem. "A Lyapunov-type inequality for a fractional q-difference boundary value problem." Journal of Nonlinear Sciences and Applications, 9, no. 5 (2016): 1965--1976
Keywords
- Lyapunov's inequality
- q-fractional derivative
- Green's function
- Mittag-Leffler function.
MSC
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