Thitiporn LinitdaSaowaluck Chasreechai2025-03-102025-03-102018Advances in Difference Equations1687183910.1186/s13662-018-1793-62-s2.0-85054787912https://repository.dusit.ac.th//handle/123456789/4922In this paper, we present some properties of the forward (_, _) -difference operators, and the existence results of two nonlocal boundary value problems for second-order forward (_, _) -difference equations. The existence and uniqueness results are proved by using the Banach fixed point theorem, and the existence of at least one positive solution is established by using the Krasnoselskii� fixed point theorem. � 2018, The Author(s).All Open Access; Gold Open AccessExistenceForward (_, _) -difference equationsNeumann boundary value problemPositive solutionArticleScopus