Fractional Elliptic and Parabolic Equations: Analysis and Related Topics

Dear Colleagues,

The fractional elliptic and parabolic equations are extensions of classical partial differential equations involving fractional derivatives. They have found widespread applications in various branches of science and have drawn more and more attention from the mathematical community. They are employed in modeling anomalous diffusion in biological systems, porous media, and materials science. Image processing benefits from their use in denoising and feature extraction, while in finance, they model long-range dependencies in financial processes. Electrochemistry applications include charge transport in batteries, and geophysics applications involve modeling seismic waves and heat conduction in the Earth's crust. Overall, fractional elliptic and parabolic equations provide enhanced accuracy in scenarios where classical models fall short or where non-local interactions are crucial and provide a powerful framework for understanding and analyzing complex systems exhibiting anomalous diffusion across various scientific fields.

In this Special Issue, we invite review and original research articles dealing with recent developments on the analysis of qualitative and quantitative properties of solutions to nonlinear fractional elliptic and parabolic equations. It will focus on, but is not limited to, the following analysis on the solutions of these equations:

• Symmetry and monotonicity of solutions;
• A priori estimates and existence of solutions;
• Uniqueness, non-existence, classifications of solutions;
• Variational methods on the existence and multiplicity of solutions;
• Regularities of solutions;
• Numerical analysis of solutions.

Prof. Dr. Wenxiong Chen
Dr. Leyun Wu
Guest Editors

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 100 words) can be sent to the Editorial Office for announcement on this website.

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.

• fractional elliptic equations
• fractional parabolic equations
• fractional laplacian
• non-local operators
• variational method
• multiplicity numerical analysis
• applications of fractional equations
• nonlinearity, symmetry, monotonicity, a priori estimate, existence, non-existence, uniqueness, classification, method of moving planes, sliding method, etc.