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On a fractional boundary value problem with fractional boundary conditions

Authors
Journal
Applied Mathematics Letters
0893-9659
Publisher
Elsevier
Volume
25
Issue
8
Identifiers
DOI: 10.1016/j.aml.2011.11.028
Keywords
  • Discrete Fractional Calculus
  • Boundary Value Problem
  • Nonlocal Boundary Conditions
  • Fractional Boundary Condition
  • Green’S Function

Abstract

Abstract In this paper, we consider a discrete fractional boundary value problem, for t∈[0,b+1]N0, of the form −Δνy(t)=f(t+ν−1,y(t+ν−1)), y(ν−2)=0, [Δαy(t)]t=ν+b−α+1=0, where f:[ν−1,…,ν+b]Nν−2×R→R is continuous, 1<ν≤2, and 0≤α<1. We prove that this problem can be interpreted as a discrete multipoint problem. We also show that the problem is a generalization of some recent results. Our results provide some basic analysis of discrete fractional boundary conditions.

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