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

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Abstract
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.
Funding Information
  • National Natural Science Foundation of China (11071143, 60904024, 61174217, JQ201119, ZR2010AL002, ZR2009AL003, J11LA01)
  • National Natural Science Foundation of China (11071143, 60904024, 61174217, JQ201119, ZR2010AL002, ZR2009AL003, J11LA01)
  • National Natural Science Foundation of China (11071143, 60904024, 61174217, JQ201119, ZR2010AL002, ZR2009AL003, J11LA01)
  • Natural Science Outstanding Youth Foundation of Shandong Province (11071143, 60904024, 61174217, JQ201119, ZR2010AL002, ZR2009AL003, J11LA01)
  • Shandong Provincial Natural Science Foundation (11071143, 60904024, 61174217, JQ201119, ZR2010AL002, ZR2009AL003, J11LA01)
  • Shandong Provincial Natural Science Foundation (11071143, 60904024, 61174217, JQ201119, ZR2010AL002, ZR2009AL003, J11LA01)
  • Natural Science Foundation of Educational Department of Shandong Province (11071143, 60904024, 61174217, JQ201119, ZR2010AL002, ZR2009AL003, J11LA01)

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