Vargas Ureña, Antonio Manuel2024-12-132024-12-132023-12-16A.M. Vargas, A Finite Difference Scheme for the Fractional Laplacian on Non-uniform Grids, Communications on Applied Mathematics and Computation https://doi.org/10.1007/s42967-023-00323-42661-8893https://doi.org/10.1007/s42967-023-00323-4https://hdl.handle.net/20.500.14468/24892The registered version of this article, first published in Communications on Applied Mathematics and Computation, is available online at the publisher's website: Springer Nature, https://doi.org/10.1007/s42967-023-00323-4La versión registrada de este artículo, publicado por primera vez en Communications on Applied Mathematics and Computation, está disponible en línea en el sitio web del editor: Springer Nature, https://doi.org/10.1007/s42967-023-00323-4In this study, we analyze the convergence of the finite difference method on non-uniform grids and provide examples to demonstrate its effectiveness in approximating fractional differential equations involving the fractional Laplacian. By utilizing non-uniform grids, it becomes possible to achieve higher accuracy and improved resolution in specific regions of interest. Overall, our findings indicate that finite difference approximation on non-uniform grids can serve as a dependable and efficient tool for approximating fractional Laplacians across a diverse array of applications.eninfo:eu-repo/semantics/openAccess12 Matemáticasartículomeshless methodfractional differential equationscaputo fractional derivative