Use of Mixed Operator Method to a fractional Hadamard Dirichlet boundary value problem


  • Lakhdar Ragoub prince mugrin university



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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How to Cite

Ragoub, L. (2023). Use of Mixed Operator Method to a fractional Hadamard Dirichlet boundary value problem. JOURNAL OF ADVANCES IN MATHEMATICS, 22, 1–9.