Multiplicity and uniqueness for a class of discrete fractional boundary value problems

[摘要] The paper deals with a class of discrete fractional boundary value problems. We construct the corresponding Green's function, analyse it in detail and establish several of its key properties. Then, by using the fixed point index theory, the existence of multiple positive solutions is obtained, and the uniqueness of the solution is proved by a new theorem on an ordered metric space established by M. Jleli, et al. (2012).

[学科分类] 应用数学

[关键词] fractional order;discrete fractional boundary value problem;fractional difference equation;positive solution