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The existence and uniqueness of solutions to boundary value problems of fractional difference equations. (English) Zbl 1264.39005
Summary: We study the existence and uniqueness of solutions for the boundary value problem -Δ v-μ v y(t)=f(t,y(t+v-1)),Δ i y(v-n)=0,i{0,,N-3},Δ N-2 y(v-N)=g(y),Δ v-N μ y(b+M+v-μ)=0, where v2,1μ<v,f:{0,,b+M}× is continuous, and nonnegative for y0,g:C([v-N,,b+M+v],) is a given function. We give a representation for the solution to this problem, and we prove the existence and uniqueness of solution to this problem by contraction mapping theorem and Brouwer theorem.
39A12Discrete version of topics in analysis
34N05Dynamic equations on time scales or measure chains
34A08Fractional differential equations