The Existence of Solutions to a System of Discrete Fractional Boundary Value Problems

Abstract EN

We study the existence of solutions for the boundary value problem -Δνy1(t)=f(y1(t+ν-1),y2(t+μ-1)), -Δμy2(t)=g(y1(t+ν-1),y2(t+μ-1)), y1(ν-2)=Δy1(ν+b)=0, y2(μ-2)=Δy2(μ+b)=0, where 1<μ,ν≤2, f,g:R×R→R are continuous functions, b∈N0.

The existence of solutions to this problem is established by the Guo-Krasnosel'kii theorem and the Schauder fixed-point theorem, and some examples are given to illustrate the main results.