Dear Colleagues,

Fractional calculus, when exploited and interpreted properly, gives us varying approaches to capturing and discovering memory effects, nonlocality, and even universality among physical quantities. Fractional deterministic and stochastic modeling enriches the fractional models that could better interpret real physical phenomena. For validating the proposed models, model calibration is of great importance and could bring chances for finding universal parameters, which integer-order models may not find. 

The Special Issue embraces the contributions regarding fractional deterministic and stochastic models, numerical techniques or theoretical justification for their calibration, and insights and outlooks (review papers) on potentials of fractional models in interpreting and discovering nature rules. The aim of the Special Issue is to attract attention of mathematicians, scientists, and engineers outside the fractional community, by providing more physical justifications for fractional models.

Potential topics include, but are not limited to

• Fractional modeling in acoustic waves, hydrodynamics, viscoelasticity, fluid/solid mechanics, turbulence, finance, biology, physics, control systems, etc.;
• Numerical methods for Fractional differential equations with random inputs;
• Numerical methods for stochastic differential equation driven by fractional Brownian motion;
• Machine learning and other inversion techniques for fractional inverse problems;
• Wellpossedness analysis of fractional inverse problems.

Dr. Guofei Pang
Dr. Wanrong Cao
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 papers will be 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 quarterly 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 1600 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 calculus modeling
• Fractional differential equations with random inputs
• Fractional PDEs
• Fractional inverse problems
• Fractional Brownian motion
• Machine learning
• Numerical methods