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چکیده
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In this paper we study the existence of unique positive solutions for the following coupled system: ⎧ ⎪⎪⎪⎪⎪⎪⎨ ⎪⎪⎪⎪⎪⎪⎩ Dα 0+ x(τ ) + f1(τ , x(τ ),Dη 0+ x(τ )) + g1(τ , y(τ )) = 0, Dβ 0+ y(τ ) + f2(τ , y(τ ),Dγ 0+ y(τ )) + g2(τ , x(τ )) = 0, τ ∈ (0, 1), n –1< α,β < n; x(i) (0) = y(i) (0) = 0, i = 0, 1, 2, ... , n – 2; [Dξ 0+ y(τ )]τ=1 = k1(y(1)), [Dζ 0+ x(τ )]τ=1 = k2(x(1)), where the integer number n > 3 and 1 ≤ γ ≤ ξ ≤ n – 2, 1 ≤ η ≤ ζ ≤ n – 2, f1, f2 : [0, 1] × R+ × R+ → R+, g1, g2 : [0, 1] × R+ → R+ and k1, k2 : R+ → R+ are continuous functions, Dα 0+ and Dβ 0+ stand for the Riemann–Liouville derivatives. An illustrative example is given to show the effectiveness of theoretical results.
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