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Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions. (English) Zbl 1211.39002
Summary: We consider a discrete fractional boundary value problem of the form - Δ ν y(t)=f(t+ν-1,y(t+ν-1)),y(ν-2)=g(y),y(ν+b)=0, where f:[ν-1,,ν+b-1] ν-2 is continuous, g:𝒞([ν-2,ν+b] ν-2 ,) is a given functional, and 1<ν2. We give a representation for the solution to this problem. Finally, we prove the existence and uniqueness of solution to this problem by using a variety of tools from nonlinear functional analysis including the contraction mapping theorem, the Brouwer theorem, and the Krasnosel’skii theorem.
MSC:
39A10Additive difference equations
26A33Fractional derivatives and integrals (real functions)
39A12Discrete version of topics in analysis
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