Special Issue "Fractional Dynamics"

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

Deadline for manuscript submissions: 31 October 2017

Special Issue Editors

Guest Editor
Prof. Dr. Carlo Cattani

Engineering School (DEIM) University of Tuscia, 01100 Largo dell'Università, Viterbo, Italy
Website | E-Mail
Interests: wavelets; fractals; fractional calculus; dynamical systems; data analysis; time series analysis; image analysis; computer science; computational methods; composite materials; elasticity; nonlinear waves
Guest Editor
Prof. Dr. Renato Spigler

Department of Mathematics and Physics, Roma Tre University, 00146 Rome, Italy
Website | E-Mail
Phone: +39-06-5733-8211
Fax: +39-06-5733-8211
Interests: fractional calculus (approximations, numerics, and applications); applied and computational mathematics

Special Issue Information

Dear Colleagues,

Modeling, simulation, and applications of Fractional Calculus have recently become an increasingly popular subject, with an impressive growth concerning applications. The founding and limited ideas on fractional derivatives have achieved an incredibly valuable status. The manifold applications in mathematics, physics, engineering, economics, biology, and medicine have opened new challenging fields of research. For instance, in mechanics, a suitable definition of the fractional operator has shed some light on viscoelasticity, by explaining memory effects on materials. Needless to say, these applications require the development of practical mathematical tools to obtain quantitative information from models, newly reformulated in terms of fractional differential equations. Even confining ourselves to the field of ordinary differential equations, the Bagley-Torvik model showed that fractional derivatives may actually arise naturally within certain physical models, and are not mere fancy mathematical generalizations.This Special Issue focuses on the most recent advances in fractional calculus, applied to dynamic problems, linear and nonlinear fractional ordinaries and partial differential equations, integral fractional differential equations and stochastic integral problems arising in all fields of science, engineering applications, and other applied fields.

Prof. Dr. Carlo Cattani
Prof. Dr. Renato Spigler
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) 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

  • mathematics
  • physics
  • mathematical physics
  • mechanics
  • fractional calculus
  • fractal
  • fractional dynamical systems
  • fractional partial differential equations

Published Papers (1 paper)

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Research

Open AccessArticle A Fractional Complex Permittivity Model of Media with Dielectric Relaxation
Fractal Fract 2017, 1(1), 4; doi:10.3390/fractalfract1010004
Received: 11 August 2017 / Revised: 25 August 2017 / Accepted: 25 August 2017 / Published: 29 August 2017
PDF Full-text (2717 KB) | HTML Full-text | XML Full-text
Abstract
In this work, we propose a fractional complex permittivity model of dielectric media with memory. Debye’s generalized equation, expressed in terms of the phenomenological coefficients, is replaced with the corresponding differential equation by applying Caputo’s fractional derivative. We observe how fractional order depends
[...] Read more.
In this work, we propose a fractional complex permittivity model of dielectric media with memory. Debye’s generalized equation, expressed in terms of the phenomenological coefficients, is replaced with the corresponding differential equation by applying Caputo’s fractional derivative. We observe how fractional order depends on the frequency band of excitation energy in accordance with the 2nd Principle of Thermodynamics. The model obtained is validated with respect to the measurements made on the biological tissues and in particular on the human aorta. Full article
(This article belongs to the Special Issue Fractional Dynamics)
Figures

Figure 1

Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Tentative title: Identifying the fractional orders in anomalous diffusion from real data
Author: Moreno Concezzi and Renato Spigler
Abstract: An attempt is made to identify the orders of the fractional derivatives in an anomalous diffusion model, starting from real data.

 

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