Opuscula Math. 38, no. 1 (2018), 31-40
https://doi.org/10.7494/OpMath.2018.38.1.31

Opuscula Mathematica

# Existence of positive solutions to a discrete fractional boundary value problem and corresponding Lyapunov-type inequalities

Amar Chidouh
Delfim F. M. Torres

Abstract. We prove existence of positive solutions to a boundary value problem depending on discrete fractional operators. Then, corresponding discrete fractional Lyapunov-type inequalities are obtained.

Keywords: fractional difference equations, Lyapunov-type inequalities, fractional boundary value problems, positive solutions.

Mathematics Subject Classification: 26A33, 26D15, 39A12.

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• Amar Chidouh
• Houari Boumedienne University, Laboratory of Dynamic Systems, Algiers, Algeria
• Delfim F. M. Torres
• Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal
• Communicated by Marek Galewski.
• Revised: 2017-05-31.
• Accepted: 2017-06-18.
• Published online: 2017-11-13.