Recent Advances in the Spatial and Temporal Discretizations of Fractional PDEs, Second Edition
A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Numerical and Computational Methods".
Deadline for manuscript submissions: 14 November 2025 | Viewed by 1243
Special Issue Editors
2. Mathematical Institute, Utrecht University, 3584 Utrecht, The Netherlands
Interests: numerical linear algebra; numerical (fractional) PDEs; parallel-in-time methods; Krylov subspace solvers
Special Issues, Collections and Topics in MDPI journals
Interests: finite difference, finite volume and finite element methods for time fractional differential equations; finite element and finite difference methods for integral fractional Laplace
Special Issues, Collections and Topics in MDPI journals
Interests: fractional calculus; fractional differential equation; variable-order; numerical method; mathematical analysis
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
Fractional PDEs (FPDEs) generalize the classic (integer-order) calculus and PDEs to any differential form of fractional orders. FPDEs are emerging as a powerful tool for modeling challenging multiscale phenomena, including overlapping microscopic and macroscopic scales, anomalous transport and long-range time–memory or spatial interactions. However, the exact solutions of FPDEs cannot be explicitly expressed; thus, numerical methods based on various spatial and temporal discretizations have become the mainstream tools for such FPDEs and have experienced a drastic development in recent decades. These spatial and temporal discretizations that maintain the important characteristics or structures of FPDEs, such as weak singularity, optimal long-time decay rate, long-term numerical stability and the convergence of numerical schemes for such FPDEs, are still limited. Therefore, developing efficient spatial and temporal discretizations for the numerical solutions of FPDEs remains challenging in the field of numerical analysis.
This Special Issue, titled “Recent Advances in the Spatial and Temporal Discretizations of Fractional PDEs, Second Edition”, 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 on topics including, but not limited to, the following:
- Finite difference, finite elements, 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 for FPDEs;
- Nonlocal modeling and computation;
- Convolution quadrature;
- Modeling and simulations involving (fractional) PDEs.
Dr. Xian-Ming Gu
Prof. Dr. Hongbin Chen
Prof. Dr. Xiangcheng Zheng
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.
Keywords
- fractional PDEs
- finite difference, finite element, finite volume, spectral methods
- nonuniform and adaptive discretizations
- adaptive space–time methods
- parallel-in-time methods
- numerical methods
- numerical treatments of integro-differential equations
- nonlocal modeling and computation
- convolution quadratures
- modeling and simulations
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