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On discrete sequential fractional boundary value problems. (English) Zbl 1236.39008

The author considers several different types of discrete sequential fractional boundary value problems. Our prototype equation is

-Δ μ 1 Δ μ 2 Δ μ 3 y(t)=f(t+μ 1 +μ 2 +μ 3 -1,y(t+μ 1 +μ 2 +μ 3 -1))

subject to the conjugate boundary conditions y(0)=0=y(b+2), where

f:[1,b+1] N 0 ×R[0,+)

is a continuous function and μ 1 ,μ 2 ,μ 3 (0,1) satisfy 1<μ 1 +μ 3 <2 and 1<μ 1 +μ 2 +μ 3 <2. He also obtains results for delta-nabla discrete fractional boundary value problems. As an application of our analysis, he gives conditions under which such problem will admit at least one positive solution.

MSC:
39A12Discrete version of topics in analysis
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