The Existence of Solutions to a System of Discrete Fractional Boundary Value Problems

The Existence of Solutions to a System of Discrete Fractional Boundary Value Problems

We study the existence of solutions for the boundary value problem -Δνy1(t)=f(y1(t+ν-1),y2(t+μ-1)), -Δμy2(t)=g(y1(t+ν-1),y2(t+μ-1)), y1(ν-2)=Δy1(ν+b)=0, y2(μ-2)=Δy2(μ+b)=0, where 1<μ,ν≤2, f,g:R×R→R are continuous functions, b∈N0. The existence of solutions to this problem is established by the Gu...

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Main Authors: Yuanyuan Pan, Zhenlai Han, Shurong Sun, Yige Zhao
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2012/707631
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spelling doaj-d7c071764d134ae1b039877ac80e2eb62020-11-25T00:53:17ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/707631707631The Existence of Solutions to a System of Discrete Fractional Boundary Value ProblemsYuanyuan Pan0Zhenlai Han1Shurong Sun2Yige Zhao3School of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, ChinaSchool of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, ChinaSchool of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, ChinaSchool of Mathematical Sciences, University of Jinan, Jinan, Shandong 250022, ChinaWe study the existence of solutions for the boundary value problem -Δνy1(t)=f(y1(t+ν-1),y2(t+μ-1)), -Δμy2(t)=g(y1(t+ν-1),y2(t+μ-1)), y1(ν-2)=Δy1(ν+b)=0, y2(μ-2)=Δy2(μ+b)=0, where 1<μ,ν≤2, f,g:R×R→R are continuous functions, b∈N0. The existence of solutions to this problem is established by the Guo-Krasnosel'kii theorem and the Schauder fixed-point theorem, and some examples are given to illustrate the main results.http://dx.doi.org/10.1155/2012/707631
collection DOAJ
language English
format Article
sources DOAJ
author Yuanyuan Pan
Zhenlai Han
Shurong Sun
Yige Zhao
spellingShingle Yuanyuan Pan
Zhenlai Han
Shurong Sun
Yige Zhao
The Existence of Solutions to a System of Discrete Fractional Boundary Value Problems
Abstract and Applied Analysis
author_facet Yuanyuan Pan
Zhenlai Han
Shurong Sun
Yige Zhao
author_sort Yuanyuan Pan
title The Existence of Solutions to a System of Discrete Fractional Boundary Value Problems
title_short The Existence of Solutions to a System of Discrete Fractional Boundary Value Problems
title_full The Existence of Solutions to a System of Discrete Fractional Boundary Value Problems
title_fullStr The Existence of Solutions to a System of Discrete Fractional Boundary Value Problems
title_full_unstemmed The Existence of Solutions to a System of Discrete Fractional Boundary Value Problems
title_sort existence of solutions to a system of discrete fractional boundary value problems
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2012-01-01
description We study the existence of solutions for the boundary value problem -Δνy1(t)=f(y1(t+ν-1),y2(t+μ-1)), -Δμy2(t)=g(y1(t+ν-1),y2(t+μ-1)), y1(ν-2)=Δy1(ν+b)=0, y2(μ-2)=Δy2(μ+b)=0, where 1<μ,ν≤2, f,g:R×R→R are continuous functions, b∈N0. The existence of solutions to this problem is established by the Guo-Krasnosel'kii theorem and the Schauder fixed-point theorem, and some examples are given to illustrate the main results.
url http://dx.doi.org/10.1155/2012/707631
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