Fractional Stochastic Process: Theory and Applications

Dear Colleagues,

This Special Issue aims to present cutting-edge multidisciplinary research on fractional stochastic processes in relation to theoretical and real-world engineering applications. We invite high-quality research papers exploring nonlinear time series, statistical methods, data analysis tools, mathematical and statistical approaches, data mining techniques in mechanics, and long-range fractal processes.

Particular attention is paid to fractal time series and fractal long-range processes in mechanics and engineering applications. Fractal time series substantially differs from conventional time series in its statistic properties. For instance, it may have a heavy-tailed probability distribution function (PDF), a slowly decayed autocorrelation function (ACF), and a power spectrum function (PSD) of 1/f type. It may have statistical dependence, long-range dependence (LRD) or short-range dependence (SRD), and global or local self-similarity.

In engineering applications, such as mechanical engineering or electronics engineering, it is usually considered as the output or response of a differential system or filter of integer order under the excitation of white noise. In this Issue, a fractal time series is taken as the solution to a differential equation of fractional order or as a response of a fractional system or a fractional filter driven by white noise in the domain of stochastic processes.

We welcome submissions of original research articles and review articles exploring theories and applications of advanced statistical and mathematical modeling and in-depth examinations of physical and mechanical systems. The articles may incorporate analytical, numerical, statistical, and experimental methodologies or a combination of these, with possible applications as follows:

Computer simulation in artificial intelligence based on fractal and fractional processes.

Mathematical modeling in the economy, management and engineering based on fractal and fractional processes.

Dr. Wanqing Song
Dr. Francesco Villecco
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.

• classic and quantum mechanics
• equilibrium and non-equilibrium
• fluids, granular and soft matter
• fractional calculus in statistical mechanics
• fractional calculus in statistical physics
• interdisciplinary statistical mechanics
• interdisciplinary statistical physics
• fault diagnosis
• life prediction
• signals processing
• neuronal signal analysis (EEG, BCI)
• mathematical modeling of diseases