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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.

39A12Discrete version of topics in analysis
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