Existence Results for Fractional Difference Equations with Three-Point Fractional Sum Boundary Conditions
We consider a discrete fractional boundary value problem of the form Δαu(t)=f(t+α-1,u(t+α-1)), t∈[0,T]ℕ0:={0,1,…,T}, u(α-2)=0, u(α+T)=Δ-βu(η+β), where 1<α≤2, β>0, η∈[α-2,α+T-1]ℕα-2:={α-2,α-1,…,α+T-1}, and f:[α-1,α,…,α+T-1]ℕα-1×ℝ→ℝ is a continuous function. The existence of at least one solu...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2013/104276 |
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| author | Thanin Sitthiwirattham Jessada Tariboon Sotiris K. Ntouyas |
| author_facet | Thanin Sitthiwirattham Jessada Tariboon Sotiris K. Ntouyas |
| author_sort | Thanin Sitthiwirattham |
| collection | DOAJ |
| description | We consider a discrete fractional boundary value problem of the form Δαu(t)=f(t+α-1,u(t+α-1)), t∈[0,T]ℕ0:={0,1,…,T}, u(α-2)=0, u(α+T)=Δ-βu(η+β), where 1<α≤2, β>0, η∈[α-2,α+T-1]ℕα-2:={α-2,α-1,…,α+T-1}, and f:[α-1,α,…,α+T-1]ℕα-1×ℝ→ℝ is a continuous function. The existence of at least one solution is proved by using Krasnoselskii's fixed point theorem and Leray-Schauder's nonlinear alternative. Some illustrative examples are also presented. |
| format | Article |
| id | doaj-art-f435621c35d14faa965e0230c874968b |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-f435621c35d14faa965e0230c874968b2025-02-03T01:07:20ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2013-01-01201310.1155/2013/104276104276Existence Results for Fractional Difference Equations with Three-Point Fractional Sum Boundary ConditionsThanin Sitthiwirattham0Jessada Tariboon1Sotiris K. Ntouyas2Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology, North Bangkok, Bangkok, ThailandDepartment of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology, North Bangkok, Bangkok, ThailandDepartment of Mathematics, University of Ioannina, 451 10 Ioannina, GreeceWe consider a discrete fractional boundary value problem of the form Δαu(t)=f(t+α-1,u(t+α-1)), t∈[0,T]ℕ0:={0,1,…,T}, u(α-2)=0, u(α+T)=Δ-βu(η+β), where 1<α≤2, β>0, η∈[α-2,α+T-1]ℕα-2:={α-2,α-1,…,α+T-1}, and f:[α-1,α,…,α+T-1]ℕα-1×ℝ→ℝ is a continuous function. The existence of at least one solution is proved by using Krasnoselskii's fixed point theorem and Leray-Schauder's nonlinear alternative. Some illustrative examples are also presented.http://dx.doi.org/10.1155/2013/104276 |
| spellingShingle | Thanin Sitthiwirattham Jessada Tariboon Sotiris K. Ntouyas Existence Results for Fractional Difference Equations with Three-Point Fractional Sum Boundary Conditions Discrete Dynamics in Nature and Society |
| title | Existence Results for Fractional Difference Equations with Three-Point Fractional Sum Boundary Conditions |
| title_full | Existence Results for Fractional Difference Equations with Three-Point Fractional Sum Boundary Conditions |
| title_fullStr | Existence Results for Fractional Difference Equations with Three-Point Fractional Sum Boundary Conditions |
| title_full_unstemmed | Existence Results for Fractional Difference Equations with Three-Point Fractional Sum Boundary Conditions |
| title_short | Existence Results for Fractional Difference Equations with Three-Point Fractional Sum Boundary Conditions |
| title_sort | existence results for fractional difference equations with three point fractional sum boundary conditions |
| url | http://dx.doi.org/10.1155/2013/104276 |
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