Applications of Finite Element Methods for Solving Fractional Partial Differential Equations

Dear Colleagues,

Fractional PDEs (FPDEs) are a generalization of classical (integer-order) PDEs that involve fractional derivatives of the dependent variables. Fractional calculus provides a natural framework for describing systems with long-range spatial or temporal interactions, anomalous transport, or memory effects that cannot be captured by classical PDEs. FPDEs have numerous applications in physics, biology, finance, and engineering. However, solving FPDEs is challenging due to the non-local nature of fractional derivatives and the lack of exact solutions in explicit form. Numerical methods based on spatial and temporal discretizations have become the main approach for solving FPDEs. Developing efficient and accurate numerical methods for solving FPDEs is an active area of research in numerical analysis. Among them, the finite element method (FEM) is an important numerical approach for solving fractional PDEs which has several advantages, including the ability to handle complex geometries and variable coefficients, and the ability to adaptively refine the mesh to improve accuracy in regions of interest.

This Special Issue will provide a platform for recent and original research results on efficient numerical methods for solving FPDEs. We invite authors to contribute original research articles for this Special Issue, “Applications of Finite Element Methods for Solving Fractional Partial Differential Equations”.

The following potential topics include, but are not limited to:

• Finite element methods;
• Other methods: finite difference, finite volume, and spectral methods;
• Nonuniform and adaptive discretizations;
• Adaptive space–time methods;
• Numerical treatments of integro-differential equations;
• Parallel-in-time methods;
• Fast matrix computations arising from numerical methods of FPDEs;
• Nonlocal modeling and computation;
• Convolution quadrature;
• Modeling and simulations involving (fractional) PDEs;
• Structure-preserving algorithms for FPDEs.

Dr. Meng Li
Dr. Yanmin Zhao
Dr. Yang Liu
Guest Editors

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• finite element methods
• fractional models
• finite difference methods
• virtual element methods
• spectral methods
• structure-preserving algorithms