Nonlinear Equations Driven by Fractional Laplacian Operators

Dear Colleagues,

Fractional Differential Equations, an extension of the usual differential equations, broaden the scope of differentiation and integration to encompass arbitrary real or complex orders. Moreover, this topic has been attracting the attention of numerous researchers due to its rich applicability across several branches of science and technology. These equations play a pivotal role in describing various phenomena, including anomalous diffusion, viscoelasticity, fractional quantum mechanics, fractional dynamical systems, control theory, signal processing, and others in the fields of physics, biology, chemistry, economics, geophysics, engineering, and beyond. Unlike classical methods, problems involving fractional operators adeptly capture non-local and memory effects in complex systems, providing accurate models where traditional approaches fall short. 

Researchers working on problems involving the fractional Laplacian operator are invited to contribute their original and high-quality work to this Special Issue, which is led by experienced researchers in the subject, fostering collaboration and pushing forward the boundaries of fractional equations. By doing so, they can contribute to the ongoing exploration and understanding of fractional calculus, consolidating cutting-edge research. This Special Issue aims to pave the way for innovative solutions and breakthroughs in the intricate new realm of equations driven by fractional operators, addressing real-world challenges and/or abstract mathematical problems.

Dr. J. Vanterler Da C. Sousa
Dr. Leandro Tavares
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 equations
• critical point theory
• monotonic arguments
• topological methods
• fixed point
• Ψ–Hilfer fractional derivative
• existence and uniqueness
• continuous dependence of solutions
• successive approximations
• Mittag–Leffler function
• generalized Mittag–Leffler function