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چکیده
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Our work is related to the existence and uniqueness of positive solution to the fractional boundary value problem(BVP) with Riemann-Liouville fractional derivative. We employ the fixed point theorem of mixed monotone operator and the attributes of the Green function to consider the following: Dν0+ u(t) = λ−1(f(t, u(t), v(t)) + g(t, u(t)) + k(t, v(t))), 0 < t < 1, 3 ≤ ν ≤ 4, u(0) = u′(0) = u′′(0) = 0,[Dρ0+ u(t)]t=1 = 0, 1 ≤ ρ ≤ 2. λ is a positive number. Dν0+ and Dρ0+ are the standard Riemann-Liouville fractional derivatives of degree ν and ρ, respectively. In the end, we provide an exemplar to illustrate the outcome. It should also be noted that in this paper we have assumed the variable v as follows v(t) = 1 − Γ(2 − ρ)t1−ρ D0ρ+u(t).
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