Use of Mixed Operator Method to a fractional Hadamard Dirichlet boundary value problem
Keywords:Mixed monotone operator, Hadamard frac- tional derivative operator, positive solution, Dirichlet boundary condition, Fractional differential equation
The purpose of this paper is to deal with the following nonlinear Hadamard fractional boundary value problem
HDα1+ u(t) + f(t, u(t), u(t)) + g(t, u(t)) = 0,
1 < t < e, 1 < α ≤ 2,
u(1) = u(e) = 0,
where HDα 1+ is the Hadamard fractional derivative operator. Using the mixed monotone operator method, we prove an existence and uniqueness result for this mixed fractional Hadamard boundary value problem. As an application of this result, we give one example to establish an existence and uniqueness of a positive solution.
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