Existence Results for Fractional Difference Equations with Three-Point Fractional Sum Boundary Conditions
2013 ◽
Vol 2013
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pp. 1-9
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Keyword(s):
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.
2011 ◽
Vol 2011
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pp. 1-19
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2021 ◽
Vol 24
(6)
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pp. 1777-1796
2018 ◽
Vol 2018
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pp. 1-12
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