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

Jleli, Mohamed¹ ; Samet, Bessem¹

¹ Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia

Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 5, p. 1965-1976.

Résumé

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.

Détail

DOI : 10.22436/jnsa.009.05.03

Classification : 26D10, 39A13, 26A33, 33E12
Keywords: Lyapunov's inequality, q-fractional derivative, Green's function, Mittag-Leffler function.

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