Manuscript Topics

Fractional partial differential equations (FPDEs) have attracted extensive attention due to their capacity to model complex physical phenomena involving anomalous diffusion, memory effects, and long-range interactions. These equations are widely used in various scientific and engineering fields, including fluid mechanics, material science, viscoelasticity, biology, and finance.

Despite their importance, the nonlocality of fractional operators brings significant challenges to analytical and numerical studies. In recent years, many efficient numerical methods have been developed, including finite difference methods, finite element methods, spectral methods, meshless approaches, fast algorithms, and machine learning-based techniques.

This special issue aims to provide a platform for researchers to present their latest research and developments in the numerical algorithms for FPDEs.

Topics of interest include, but are not limited to:
- Novel numerical schemes for space-, time-, and space-time fractional PDEs
- High-order, adaptive, or structure-preserving algorithms
- Efficient solvers and fast algorithms for large-scale FPDEs
- Error analysis and stability studies
- Numerical methods for fractional models in heterogeneous or random media
- Applications of FPDEs in science and engineering
- Machine learning or data-driven approaches for fractional models

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