Special Issue "The Craft of Fractional Modelling in Science and Engineering 2018"

A special issue of Fractal and Fractional (ISSN 2504-3110).

Deadline for manuscript submissions: closed (1 December 2018)

Special Issue Editor

Guest Editor
Prof. Dr. Jordan Hristov

Department of Chemical Engineering, University of Chemical Technology and Metallurgy, 1756 Sofia, Bulgaria
Website 1 | Website 2 | Website 3 | E-Mail
Interests: non-lineat transport phenomena; modelling; scaling; fractional calculus; heat and mass transfer; diffusion problems

Special Issue Information

Dear Colleagues,

Fractional calculus has performed an important role in the fields of mathematics, physics, electronics, mechanics, and engineering in recent years. Modelling methods involving fractional operators are continuously generalized and enhanced, especially during the last few decades. Many operations in physics and engineering can be defined accurately using systems of differential equations containing different types of fractional derivatives.

The goal of this Special Issue is to report the latest progress and to present craft of fractional modelling in science and engineering We therefore invite researchers working within fields of theory, methods, and applications of these problems to submit their latest findings to this Special Issue.

The best articles from the collection will be selected by the guest-editor and the editorial board and will be published as a book,

The main topics of the collections include, but are not limited to:

  • Fractional modelling: Broad aspects
  • Solution techniques: Analytical and numerical;
  • Memory kernels: Identification, construction and definitions of new fractional operators
  • Diffusion models
  • Local fractional calculus
  • Discrete fractional calculus
  • Heat, mass and momentum transfer (fluid dynamics) with relaxations
  • Mechanics and rheology of solid materials
  • Nano-applications of fractional modelling
  • Biomechanical and biomedical applications of fractional calculus
  • Chaos and complexity
  • Thermodynamic compatibility of fractional models
  • Control problems and model identifications with fractional operators
  • Electrochemical systems and alternative energy sources

Prof. Dr. Jordan Hristov
Guest Editor

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) is waived for well-prepared manuscripts submitted to this issue. 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 modelling
  • applied models
  • solution techniques
  • memory kernels
  • fractional operator definitions
  • biomechanical and medical applications
  • control and identification
  • local fractional calculus
  • discrete fractional calculus
  • electrochemical systems

Published Papers (5 papers)

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Research

Open AccessArticle
Integral Representations and Algebraic Decompositions of the Fox-Wright Type of Special Functions
Fractal Fract 2019, 3(1), 4; https://doi.org/10.3390/fractalfract3010004
Received: 23 December 2018 / Revised: 22 January 2019 / Accepted: 22 January 2019 / Published: 25 January 2019
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Abstract
The manuscript surveys the special functions of the Fox-Wright type. These functions are generalizations of the hypergeometric functions. Notable representatives of the type are the Mittag-Leffler functions and the Wright function. The integral representations of such functions are given and the conditions under [...] Read more.
The manuscript surveys the special functions of the Fox-Wright type. These functions are generalizations of the hypergeometric functions. Notable representatives of the type are the Mittag-Leffler functions and the Wright function. The integral representations of such functions are given and the conditions under which these function can be represented by simpler functions are demonstrated. The connection with generalized Erdélyi-Kober fractional differential and integral operators is demonstrated and discussed. Full article
(This article belongs to the Special Issue The Craft of Fractional Modelling in Science and Engineering 2018)
Open AccessArticle
Regularized Integral Representations of the Reciprocal Gamma Function
Fractal Fract 2019, 3(1), 1; https://doi.org/10.3390/fractalfract3010001
Received: 16 November 2018 / Revised: 29 December 2018 / Accepted: 8 January 2019 / Published: 12 January 2019
Cited by 1 | PDF Full-text (340 KB) | HTML Full-text | XML Full-text
Abstract
This paper establishes a real integral representation of the reciprocal Gamma function in terms of a regularized hypersingular integral along the real line. A regularized complex representation along the Hankel path is derived. The equivalence with the Heine’s complex representation is demonstrated. For [...] Read more.
This paper establishes a real integral representation of the reciprocal Gamma function in terms of a regularized hypersingular integral along the real line. A regularized complex representation along the Hankel path is derived. The equivalence with the Heine’s complex representation is demonstrated. For both real and complex integrals, the regularized representation can be expressed in terms of the two-parameter Mittag-Leffler function. Reference numerical implementations in the Computer Algebra System Maxima are provided. Full article
(This article belongs to the Special Issue The Craft of Fractional Modelling in Science and Engineering 2018)
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Open AccessArticle
Mathematical Modeling of Solutes Migration under the Conditions of Groundwater Filtration by the Model with the k-Caputo Fractional Derivative
Fractal Fract 2018, 2(4), 28; https://doi.org/10.3390/fractalfract2040028
Received: 1 October 2018 / Revised: 20 October 2018 / Accepted: 23 October 2018 / Published: 24 October 2018
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Abstract
Within the framework of a new mathematical model of convective diffusion with the k-Caputo derivative, we simulate the dynamics of anomalous soluble substances migration under the conditions of two-dimensional steady-state plane-vertical filtration with a free surface. As a corresponding filtration scheme, we [...] Read more.
Within the framework of a new mathematical model of convective diffusion with the k-Caputo derivative, we simulate the dynamics of anomalous soluble substances migration under the conditions of two-dimensional steady-state plane-vertical filtration with a free surface. As a corresponding filtration scheme, we consider the scheme for the spread of pollution from rivers, canals, or storages of industrial wastes. On the base of a locally one-dimensional finite-difference scheme, we develop a numerical method for obtaining solutions of boundary value problem for fractional differential equation with k-Caputo derivative with respect to the time variable that describes the convective diffusion of salt solution. The results of numerical experiments on modeling the dynamics of the considered process are presented. The results that show an existence of a time lag in the process of diffusion field formation are presented. Full article
(This article belongs to the Special Issue The Craft of Fractional Modelling in Science and Engineering 2018)
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Open AccessArticle
Power Laws in Fractionally Electronic Elements
Fractal Fract 2018, 2(4), 24; https://doi.org/10.3390/fractalfract2040024
Received: 28 August 2018 / Revised: 10 September 2018 / Accepted: 21 September 2018 / Published: 26 September 2018
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Abstract
The highlight presented in this short article is about the power laws with respect to fractional capacitance and fractional inductance in terms of frequency. Full article
(This article belongs to the Special Issue The Craft of Fractional Modelling in Science and Engineering 2018)
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Open AccessArticle
Non-Gaussian Distributions to Random Walk in the Context of Memory Kernels
Fractal Fract 2018, 2(3), 20; https://doi.org/10.3390/fractalfract2030020
Received: 13 July 2018 / Revised: 24 July 2018 / Accepted: 27 July 2018 / Published: 29 July 2018
Cited by 13 | PDF Full-text (965 KB) | HTML Full-text | XML Full-text
Abstract
The investigation of diffusive process in nature presents a complexity associated with memory effects. Thereby, it is necessary new mathematical models to involve memory concept in diffusion. In the following, I approach the continuous time random walks in the context of generalised diffusion [...] Read more.
The investigation of diffusive process in nature presents a complexity associated with memory effects. Thereby, it is necessary new mathematical models to involve memory concept in diffusion. In the following, I approach the continuous time random walks in the context of generalised diffusion equations. To do this, I investigate the diffusion equation with exponential and Mittag-Leffler memory-kernels in the context of Caputo-Fabrizio and Atangana-Baleanu fractional operators on Caputo sense. Thus, exact expressions for the probability distributions are obtained, in that non-Gaussian distributions emerge. I connect the distribution obtained with a rich class of diffusive behaviour. Moreover, I propose a generalised model to describe the random walk process with resetting on memory kernel context. Full article
(This article belongs to the Special Issue The Craft of Fractional Modelling in Science and Engineering 2018)
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