A Lyapunov-type inequality for a fractional q-difference boundary value problem

Volume 9, Issue 5, pp 1965--1976 http://dx.doi.org/10.22436/jnsa.009.05.03

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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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Keywords

• Lyapunov's inequality
• q-fractional derivative
• Green's function
• Mittag-Leffler function.

MSC

•  26D10
•  39A13
•  26A33
•  33E12

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