TY - JOUR
T1 - Existence and Uniqueness Results for Solutions to Fractional $p(·, ·)$-Laplacian Problems with a Variable-Order Derivative
AU - Azghay , Abdelilah
AU - Massar , Mohammed
AU - Mhouti , Abderrahim El
JO - Journal of Nonlinear Modeling and Analysis
VL - 4
SP - 1482
EP - 1496
PY - 2025
DA - 2025/07
SN - 7
DO - http://doi.org/10.12150/jnma.2025.1482
UR - https://global-sci.org/intro/article_detail/jnma/24247.html
KW - Fractional $p(·, ·)$-Laplacian, uniqueness, monotone operator theory, variational methods.
AB - <p style="text-align: justify;">This paper investigates a class of fractional problems involving
the variable-order $p(·, ·)$-Laplacian with homogeneous Dirichlet boundary conditions. Under suitable assumptions on the nonlinear term, we establish novel
existence 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.</p>