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Volume 7, Issue 4
Existence and Uniqueness Results for Solutions to Fractional $p(·, ·)$-Laplacian Problems with a Variable-Order Derivative

Abdelilah Azghay, Mohammed Massar & Abderrahim El Mhouti

DOI: 10.12150/jnma.2025.1482

J. Nonl. Mod. Anal., 7 (2025), pp. 1482-1496.

Published online: 2025-07

[An open-access article; the PDF is free to any online user.]

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  • Abstract

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.

  • Keywords

Fractional $p(·, ·)$-Laplacian, uniqueness, monotone operator theory, variational methods.

  • AMS Subject Headings

35A15, 35D30, 35J35, 35J60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-7-1482, author = {Azghay , AbdelilahMassar , Mohammed and Mhouti , Abderrahim El}, title = {Existence and Uniqueness Results for Solutions to Fractional $p(·, ·)$-Laplacian Problems with a Variable-Order Derivative}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2025}, volume = {7}, number = {4}, pages = {1482--1496}, abstract = {

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.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.1482}, url = {http://global-sci.org/intro/article_detail/jnma/24247.html} }
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 -

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.

Azghay , AbdelilahMassar , Mohammed and Mhouti , Abderrahim El. (2025). Existence and Uniqueness Results for Solutions to Fractional $p(·, ·)$-Laplacian Problems with a Variable-Order Derivative. Journal of Nonlinear Modeling and Analysis. 7 (4). 1482-1496. doi:10.12150/jnma.2025.1482
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