Recent Advances in Nonlocal Problems Involving the Fractional Laplacian Operators
A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "General Mathematics, Analysis".
Deadline for manuscript submissions: 14 August 2025 | Viewed by 1635
Special Issue Editor
Interests: fractional differential equations; partial differential equations; variational principle; fractional Laplacian
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
The study of fractional Sobolev spaces and their corresponding nonlocal equations has been exposed to tremendous popularity, since it not only involves mathematical challenges (in particular, inhomogeneity) but also many applications. This Special Issue will focus on new aspects of the recent developments in the theory and applications of fractional Laplacian equations, stationary problems involving singular nonlinearities, nonlocal problems with variable exponents, and problems involving the fractional magnetic operator, subject to various boundary conditions.
Contributions to the Special Issue may address (but are not limited) to the following aspects:
- Existence and multiplicity of solutions of fractional differential equations;
- Existence and multiplicity of solutions of nonlocal problems with variable exponent;
- Existence and multiplicity of solutions of nonlocal problems of Kirchhoff type;
- Stationary problems involving singular nonlinearities;
- Regularity of solutions for fractional differential equations.
Dr. Yun-Ho Kim
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 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.
Keywords
- fractional differential equations
- fractional Sobolev spaces
- variable exponent elliptic operator
- fractional Laplacian problems with the external magnetic field
- variational methods on the existence and multiplicity of solutions
- a priori estimates and existence of solutions
- uniqueness, non-existence, classifications of solutions
- critical point theorem on the existence and multiplicity of solutions
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