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Fractal Fract
Special Issues
Recent Advances in Fractal and Fractional Calculus Theory and Its...
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Recent Advances in Fractal and Fractional Calculus Theory and Its Applications

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

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 3087

Special Issue Editors

Dr. Aboutrab A. Aliverdiev

E-Mail Website
Guest Editor
IGR&RE, Filial of Joint Institute for High Temperatures of Russian Academy of Sciences, Dagestan State University, Makhachkala, Russia
Interests: mathematical modeling; fractional calculus; image analysis; thermal physics; phase transitions; plasma physics; laser-driven shocks; extreme states
Prof. Dr. Jordan Hristov

E-Mail Website1 Website2
Guest Editor
Department of Chemical Engineering, University of Chemical Technology and Metallurgy, 1756 Sofia, Bulgaria
Interests: mathematical modeling; fractional calculus; non-linear diffusion; viscoelasticity
Special Issues, Collections and Topics in MDPI journals
Dr. Vetlugin Beibelaev

E-Mail Website
Guest Editor
1. Institute for Geothermal Research and Renewable Energy, a Branch of the Joint Institute for High Temperatures, Russian Academy of Sciences, 367030 Makhachkala, Russia
2. Applied Mathematics, Dagestan State University, 367025 Makhachkala, Russia
Interests: mathematical modeling; fractional calculus; thermal conductivity of rocks

Special Issue Information

Dear Colleagues,

Fractals and the closely related fields of fractional differentiation and integration (fractional calculus) are young but rapidly developing areas of research that have been the focus of theoretical work and implemented in a wide range of applications.

This Special Issue aims to further advance research on the latest achievements and applications of fractal theory, including chaos theory, fractional calculus and their applications in the modeling of various phenomena of biology, medicine (including the spread of epidemics), heat and mass transfer in media with reduced dimensionality and, as a consequence, memory and spatial correlation effects, etc.

Topics of interest for this issue include (but are not limited to):

  • Chaos theory;
  • Fractal algorithms;
  • Fractional calculus;
  • Memory kernels;
  • Non-locality and hereditary effects;
  • Transient phenomena with hereditary;
  • Fractional operator applications;
  • Epidemiological challenges and contemporary issues related to pandemics; 
  • Environmental hereditary.

Dr. Aboutrab A. Aliverdiev
Prof. Dr. Jordan Hristov
Dr. Vetlugin Beibelaev
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.

Keywords

  • fractional calculus
  • memory kernels
  • non-locality and hereditary effects
  • transient phenomena with hereditary
  • fractional operator applications
  • epidemiological challenges and contemporary issues related to pandemics
  • environmental hereditary

Published Papers (2 papers)

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Research

23 pages, 4060 KiB  
Article
Transient Heat Conduction in a Semi-Infinite Domain with a Memory Effect: Analytical Solutions with a Robin Boundary Condition
by Vetlugin Dzhabrailovich Beybalaev, Abutrab Aleksandrovich Aliverdiev and Jordan Hristov
Fractal Fract. 2023, 7(10), 770; https://doi.org/10.3390/fractalfract7100770 - 20 Oct 2023
Viewed by 1395
Abstract
The Robin boundary condition initial value problem for transient heat conduction with the time-fractional Caputo derivative in a semi-infinite domain with a convective heat transfer (Newton’s law) at the boundary has been solved and analyzed by two analytical approaches. The uniqueness and the [...] Read more.
The Robin boundary condition initial value problem for transient heat conduction with the time-fractional Caputo derivative in a semi-infinite domain with a convective heat transfer (Newton’s law) at the boundary has been solved and analyzed by two analytical approaches. The uniqueness and the stability of the solution on the half-axis have been analyzed. The problem solutions by application of the operational method (Laplace transform in the time domain) and the integral-balance method (double integration technique) have been developed analytically. Full article
(This article belongs to the Special Issue Recent Advances in Fractal and Fractional Calculus Theory and Its Applications)
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11 pages, 686 KiB  
Article
Mathematical Model of Heat Conduction for a Semi-Infinite Body, Taking into Account Memory Effects and Spatial Correlations
by Vetlugin D. Beybalaev, Abutrab A. Aliverdiev, Amuchi Z. Yakubov, Said A. Ninalalov and Anise A. Amirova
Fractal Fract. 2023, 7(3), 265; https://doi.org/10.3390/fractalfract7030265 - 16 Mar 2023
Cited by 1 | Viewed by 993
Abstract
One of the promising approaches to the description of many physical processes is the use of the fractional derivative mathematical apparatus. Fractional dimensions very often arise when modeling various processes in fractal (multi-scale and self-similar) environments. In a fractal medium, in contrast to [...] Read more.
One of the promising approaches to the description of many physical processes is the use of the fractional derivative mathematical apparatus. Fractional dimensions very often arise when modeling various processes in fractal (multi-scale and self-similar) environments. In a fractal medium, in contrast to an ordinary continuous medium, a randomly wandering particle moves away from the reference point more slowly since not all directions of motion become available to it. The slowdown of the diffusion process in fractal media is so significant that physical quantities begin to change more slowly than in ordinary media.This effect can only be taken into account with the help of integral and differential equations containing a fractional derivative with respect to time. Here, the problem of heat and mass transfer in media with a fractal structure was posed and analytically solved when a heat flux was specified on one of the boundaries. The second initial boundary value problem for the heat equation with a fractional Caputo derivative with respect to time and the Riesz derivative with respect to the spatial variable was studied. A theorem on the semigroup property of the fractional Riesz derivative was proved. To find a solution, the problem was reduced to a boundary value problem with boundary conditions of the first kind. The solution to the problem was found by applying the Fourier transform in the spatial variable and the Laplace transform in time. A computational experiment was carried out to analyze the obtained solutions. Graphs of the temperature distribution dependent on the coordinate and time were constructed. Full article
(This article belongs to the Special Issue Recent Advances in Fractal and Fractional Calculus Theory and Its Applications)
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