Abstract
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).
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The research has been supported by the National Natural Science Foundation of China under Grants 71272066 and 71210003.
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Lv, Z., Gong, Y. & Chen, Y. Multiplicity and uniqueness for a class of discrete fractional boundary value problems. Appl Math 59, 673–695 (2014). https://doi.org/10.1007/s10492-014-0079-x
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DOI: https://doi.org/10.1007/s10492-014-0079-x
Keywords
- fractional order
- discrete fractional boundary value problem
- fractional difference equation
- positive solution