Published January 1, 2013
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Existence Results for Fractional Difference Equations with Three-Point Fractional Sum Boundary Conditions
- 1. King Mongkut's University of Technology North Bangkok
- 2. University of Ioannina
Description
We consider a discrete fractional boundary value problem of the formΔαu(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),where1<α≤2,β>0,η∈[α-2,α+T-1]ℕα-2:={α-2,α-1,…,α+T-1}, andf:[α-1,α,…,α+T-1]ℕα-1×ℝ→ℝis 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.
Translated Descriptions
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This is an automatic machine translation with an accuracy of 90-95%
Translated Description (Arabic)
نحن نعتبر مسألة القيمة الحدية الكسرية المنفصلة للشكلΔαu (t) = f (t + α - 1, u (t + α-1)), t?????????????????????????????→????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? تم إثبات وجود حل واحد على الأقل باستخدام نظرية النقطة الثابتة لكراسنوسيلسكي وبديل ليراي شودر غير الخطي. كما يتم تقديم بعض الأمثلة التوضيحية.Translated Description (French)
Nous considérons un problème de valeur limite fractionnaire discrète de la formeΔαu(t)=f(t+α-1,u(t+α-1)), t∈[0,T] 0 :={0,1,…,T}, u(α-2)=0, u(α+T)=Δ-βu(η+β),où1<α≤2,β>0,η∈[α-2,α+T-1] α-2 :={α-2,α-1,…,α+T-1}, etf :[α-1,α, …,α+T-1] α-1→× ‹ est une fonction continue. L'existence d'au moins une solution est prouvée en utilisant le théorème du point fixe de Krasnoselskii et l'alternative non linéaire de Leray-Schauder. Quelques exemples illustratifs sont également présentés.Translated Description (Spanish)
Consideramos un problema de valor de límite fraccionario discreto de la formaΔαu(t)=f(t+α-1,u(t+α-1)), t∈[0,T] "0:={0,1,…, T}, u(α-2)=0, u(α+T)=Δ-βu(η + β),donde1<α≤2, β>0, η∈[α-2, α +T - 1]" α-2:={α- 2,α -1, …, α +T - 1}, yf:[α -1, α, …, α→ +T -1] es una función continua. La existencia de al menos una solución se demuestra utilizando el teorema del punto fijo de Krasnoselskii y la alternativa no lineal de Leray-Schauder. También se presentan algunos ejemplos ilustrativos.Files
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Additional details
Additional titles
- Translated title (Arabic)
- نتائج وجود معادلات الفرق الكسري مع شروط حدود المجموع الكسري ثلاثي النقاط
- Translated title (French)
- Résultats d'existence pour les équations de différence fractionnaire avec des conditions de limite de somme fractionnaire à trois points
- Translated title (Spanish)
- Resultados de existencia para ecuaciones de diferencia fraccionaria con condiciones de límite de suma fraccionaria de tres puntos
Identifiers
- Other
- https://openalex.org/W2067794579
- DOI
- 10.1155/2013/104276
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