New Insights into Random Walks and Diffusion Equations

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Probability and Statistics".

Deadline for manuscript submissions: 18 July 2024 | Viewed by 118

Special Issue Editors

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Guest Editor
Department of Biomolecular Sciences of FCFRP, University of São Paulo, Ribeirão Preto, SP, Brazil
Interests: statistical and biological physics; monte carlo simulation; diffusive and growth processes; random walks

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Guest Editor
Instituto de Física, Universidade Federal de Alagoas, Maceió, AL, Brazil
Interests: statistical and biological physics; diffusive processes; random walks

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Guest Editor
Department of Theoretical and Experimental Physics, Universidade Federal do Rio Grande do Norte, Natal, Brazil
Interests: lévy flights; random walks; statistical mechanics
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Special Issue Information

Dear Colleagues,

Random walks (RWs) are defined as stochastic processes that consist of a sequence of random steps determining the paths of a walker. These processes can be categorized as either Markovian or non-Markovian, in discrete or continuous time domains. Many natural phenomena can be effectively modeled using RWs, such as normal as well as anomalous diffusion. The applications of RWs span a wide range of scientific fields, including economics, biology, ecology, social sciences, physics, and chemistry. In general, diffusion equations in terms of probability densities can be derived for RWs. Resolving them often necessitates computational simulations, especially in cases of higher complexity.

We invite researchers to submit original research or review articles on recent developments in random walks and diffusion equations. This invitation applies to both discrete and continuous time domains, with a potential emphasis on theoretical and/or applied aspects.

Topics include, but are not limited to, the following:

  • Continuous-time random walks (CTRW);
  • Fractional diffusion equations;
  • Discrete-time non-Markovian random walks;
  • Diffusion equations for discrete-time non-Markovian random walks;
  • Self-reinforced random walks;
  • Anomalous diffusion.

Dr. Marco Antonio Alves Da Silva
Prof. Dr. José Carlos Cressoni
Prof. Dr. Gandhimohan M. Viswanathan
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at 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.


  • continuous-time random walks
  • discrete-time random walks
  • diffusion equations
  • fractional diffusion equations
  • anomalous diffusion
  • computer simulation
  • markovian processes
  • non-markovian processes

Published Papers

This special issue is now open for submission.
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