Existence and Uniqueness Results for Solutions to Fractional $p(·, ·)$-Laplacian Problems with a Variable-Order Derivative (Journal of Nonlinear Modeling and Analysis, 2025)
This paper investigates a class of fractional problems involvingthe variable-order $p(·, ·)$-Laplacian with homogeneous Dirichlet boundary conditions. Under suitable assumptions on the nonlinear term, we establish novelexistence and uniqueness results for weak solutions. We achieve this by combining variational techniques with a result from the theory of monotone operators. Additionally, we reveal several interesting properties of the solution.