Special Issue "Modelling Problems Arising in Science and Engineering with Fractional Differential Operators: Beyond the Power-Law Limit"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 31 December 2019

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,

You are kindly invited to contribute to the Special Issue “Modelling Problems Arising in Science and Engineering with Fractional Differential Operators: Beyond the Power-Law Limit”.

Fractional calculus has a brilliant history in the modelling of non-linear and anomalous problems in mathematics, physics, statistics and engineering, involving a variety of fractional-order integral and derivative operators, such as the ones named after Grunwald-Letnikov, Riemann-Liouville, Weyl, Caputo, Hadamard, Riesz, Erdelyi-Kober, etc., based on the power-law memory. Beyond this bright classical basis, in recent years new trends in fractional modelling involving operators with non-singular kernels have been created to model dissipative phenomena that cannot be adequately modelled by fractional differential operators based on singular kernels.

This Special Issue addresses contemporary modeling problems in science and engineering involving fractional differential operators with classical and new memory kernels. This is a call to authors involved in modeling with new and classical fractional differential operators to show their important positions in fractional modelling theory, differences in applications and how these operators should be applied. The issue offers a broad range of applied topics and multidisciplinary applications of fractional order differential operators with classical and new kernels in science and engineering.

We invite and welcome review, expository, and original research articles dealing with recent advances in the theory of fractional-order integral and derivative operators and their multidisciplinary applications. We will be glad to see your contributions with strong results demonstrating the feasibility of both the classical and the new trends in fractional calculus.

The main topics of the collections envisage some principle problems, including but not limited to:

  • Fractional modelling: new trends, new fractional operators, mathematical properties of fractional operators,
  • Memory kernels to fractional operators: identification, construction, definitions of fractional operators on their basis and relevant properties
  • Fractional-order ODEs, PDEs and integro-differential equations involving new fractional operators
  • Special functions of mathematical physics and applied mathematics associated with the new fractional operators
  • Examples beyond the classical singular kernel applications: Non-power-law relaxations involving new operators
  • Fractional modelling of the mechanics and rheology of solid materials with non-power-law relaxations
  • Anomalous diffusion models beyond the power-law behaviour
  • Fractional modelling for biomechanical and biomedical applications with new operators
  • Thermodynamic compatibility of fractional models with new kernels
  • Fractional models of heat, mass and fluid flow beyond the power-law
  • Control and signal fractional modelling problems with non-singular fractional operators
  • Dynamic and stochastic systems based on fractional calculus with non-power-law kernels
  • Fractional modelling of electrochemical and magnetic systems with non-singular operators

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. Mathematics 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 850 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 modelling with non-power-law kernels
  • Fractional operator definitions and properties
  • Fractional-order ODEs, PDEs and integro-differential equations
  • Non-power-law relaxations involving new operators
  • Rheological modeling of fluid and solids with non-singular kernels
  • Anomalous diffusion transport beyond the power-law
  • Biomechanical and medical models with non-singular fractional operators
  • Thermodynamical model consistency when non-singular operators are involved
  • Control and identification with new fractional operators
  • Chaos and complexity with non-singular fractional operators

Published Papers (1 paper)

View options order results:
result details:
Displaying articles 1-1
Export citation of selected articles as:

Research

Open AccessArticle
New Numerical Aspects of Caputo-Fabrizio Fractional Derivative Operator
Mathematics 2019, 7(4), 374; https://doi.org/10.3390/math7040374
Received: 3 March 2019 / Revised: 16 April 2019 / Accepted: 17 April 2019 / Published: 24 April 2019
PDF Full-text (3673 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, a new definition for the fractional order operator called the Caputo-Fabrizio (CF) fractional derivative operator without singular kernel has been numerically approximated using the two-point finite forward difference formula for the classical first-order derivative of the function f (t [...] Read more.
In this paper, a new definition for the fractional order operator called the Caputo-Fabrizio (CF) fractional derivative operator without singular kernel has been numerically approximated using the two-point finite forward difference formula for the classical first-order derivative of the function f (t) appearing inside the integral sign of the definition of the CF operator. Thus, a numerical differentiation formula has been proposed in the present study. The obtained numerical approximation was found to be of first-order convergence, having decreasing absolute errors with respect to a decrease in the time step size h used in the approximations. Such absolute errors are computed as the absolute difference between the results obtained through the proposed numerical approximation and the exact solution. With the aim of improved accuracy, the two-point finite forward difference formula has also been utilized for the continuous temporal mesh. Some mathematical models of varying nature, including a diffusion-wave equation, are numerically solved, whereas the first-order accuracy is not only verified by the error analysis but also experimentally tested by decreasing the time-step size by one order of magnitude, whereupon the proposed numerical approximation also shows a one-order decrease in the magnitude of its absolute errors computed at the final mesh point of the integration interval under consideration. Full article
Figures

Figure 1

Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top