Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
473683 | Computers & Mathematics with Applications | 2011 | 12 Pages |
Abstract
In this paper, we consider a discrete fractional boundary value problem of the form −Δνy(t)=f(t+ν−1,y(t+ν−1))−Δνy(t)=f(t+ν−1,y(t+ν−1)), y(ν−2)=g(y)y(ν−2)=g(y), y(ν+b)=0y(ν+b)=0, where f:[ν−1,…,ν+b−1]Nν−2×R→Rf:[ν−1,…,ν+b−1]Nν−2×R→R is continuous, g:C([ν−2,ν+b]Nν−2,R)g:C([ν−2,ν+b]Nν−2,R) is a given functional, and 1<ν≤21<ν≤2. We give a representation for the solution to this problem. Finally, we prove the existence and uniqueness of solution to this problem by using a variety of tools from nonlinear functional analysis including the contraction mapping theorem, the Brouwer theorem, and the Krasnosel’skii theorem.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
Christopher S. Goodrich,