Space-Fractional Diffusion Equations and Applications

Dear Colleagues,

Fractional calculus has emerged as a powerful tool for modeling complex physical phenomena that exhibit non-local behavior and memory effects, which cannot be adequately described by classical integer-order derivatives. Among these, space-fractional diffusion equations have gained significant attention for their ability to model anomalous diffusion processes in heterogeneous media, such as porous materials, biological tissues, and financial markets. These equations provide a more accurate representation of transport mechanisms where particle jumps follow heavy-tailed distributions (Lévy flights).

However, solving space-fractional diffusion equations presents substantial mathematical and computational challenges due to the non-local nature of fractional operators. Developing efficient, stable, and high-order numerical methods remains a critical area of research to bridge the gap between theoretical models and practical applications.

Aim and Scope:

This Special Issue aims to present and disseminate the most recent advances in the theory, numerical analysis, and applications of fractional diffusion equations. We particularly encourage submissions focusing on space-fractional derivatives and innovative computational techniques. We invite contributions addressing, but not limited to, the following topics:

• Space-fractional diffusion and advection-diffusion equations;

• Finite difference, finite element, and spectral methods for fractional PDEs;

• Fast algorithms and parallel computing for non-local operators;

• Inverse problems and parameter identification in fractional models;

• Applications in physics, biology, engineering, and finance;

• Stability and convergence analysis of numerical schemes.

We look forward to receiving your valuable contributions.

Prof. Dr. Muzhou Hou
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

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-anonymized 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.

• fractional diffusion equations
• space-fractional derivatives
• numerical methods
• anomalous diffusion
• finite difference methods
• finite element methods
• spectral methods
• non-local operators
• computational mathematics
• mathematical modeling