Mathematical Problems in Engineering

New Challenges in Fractional Systems


Publishing date
29 Mar 2013
Status
Published
Submission deadline
09 Nov 2012

1University of Bordeaux 1, Bordeaux, France

2Ghent University, Ghent, Belgium

3Óbuda University, Budapest, Hungary


New Challenges in Fractional Systems

Description

Fractional order differentiation consists in the generalization of classical integer differentiation to real or complex orders. From a mathematical point of view, several interpretations of fractional differentiation were proposed, but there is still a deep debate about it. The fractional differentiation and fractional integration are nonlocal operations based on an integral with a singular kernel. This explains why these operators are still not well defined and that several definitions still coexist. Since the first recorded reference work in 1695 up to the present day, many papers have been published on this subject, but much progress still to be done particularly on the relationship of these different definitions with the physical reality of a system.

A fractional order system is a system described by an integrodifferential equation involving fractional order derivatives of its input(s) and/or output(s). From a physical point of view, linear fractional derivatives and integrals order systems are not classical linear systems and not quite conventional distributed parameter systems. They are in fact halfway between these two classes of systems and are a modelling tool well suited to a wide class of phenomena with nonstandard dynamic behaviour, and the applications of fractional order systems are now well accepted in the following disciplines:

  • Signal processing (filtering, restoration, reconstruction, analysis of fractal noises, etc.)
  • Image processing (fractal environment modelling, pattern recognition, edge detection, etc.)
  • Economy (analysis of stock exchange signals, etc.)
  • Electrical engineering (modelling of motors, transformers, skin effect, etc.)
  • Electronics, telecommunications (phase locking loops, etc.)
  • Electromagnetism (modelling of complex dielectric materials, etc.)
  • Electrochemistry (modelling of batteries and ultracapacitors, etc.)
  • Thermal engineering (modelling and identification of thermal systems, etc.)
  • Mechanics, mechatronics (viscoelasticity, vibration insulation, etc.)
  • Automatic control (system identification, observation, and control of fractional systems, etc.)
  • Biology, biophysics (signal and models of biological systems, viscoelasticity in biology, etc.)
  • Physics (analysis and modelling of diffusion phenomenon, etc.)

The goal of the present special issue is to address the latest developments in the area of fractional calculus application in signals and systems. Papers describing original research work that reflects the recent theoretical advances and experimental results as well as open new avenues for research are invited on all aspects of object tracking.

Before submission authors should carefully read over the journal's Author Guidelines, which are located at http://www.hindawi.com/journals/mpe/guidelines/. Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at http://mts.hindawi.com/ according to the following timetable:


Articles

  • Special Issue
  • - Volume 2013
  • - Article ID 239378
  • - Editorial

New Challenges in Fractional Systems

Jocelyn Sabatier | Clara Ionescu | ... | José A. Tenreiro Machado
  • Special Issue
  • - Volume 2013
  • - Article ID 932150
  • - Research Article

A New Model of the Fractional Order Dynamics of the Planetary Gears

Vera Nikolic-Stanojevic | Ljiljana Veljovic | Cemal Dolicanin
  • Special Issue
  • - Volume 2013
  • - Article ID 642101
  • - Research Article

Parametric Analysis of a Heavy Metal Sorption Isotherm Based on Fractional Calculus

Enrico M. Gomes | Rosana R. L. Araújo | ... | Ervin K. Lenzi
  • Special Issue
  • - Volume 2013
  • - Article ID 356215
  • - Review Article

Stability of Fractional Order Systems

Margarita Rivero | Sergei V. Rogosin | ... | Juan J. Trujillo
  • Special Issue
  • - Volume 2013
  • - Article ID 498781
  • - Research Article

Existence Results for a Coupled System of Nonlinear Singular Fractional Differential Equations with Impulse Effects

Yuji Liu | Juan J. Nieto | Óscar Otero-Zarraquiños
  • Special Issue
  • - Volume 2013
  • - Article ID 895640
  • - Research Article

Fractional-Order Generalized Predictive Control: Application for Low-Speed Control of Gasoline-Propelled Cars

M. Romero | A. P. de Madrid | ... | B. M. Vinagre
  • Special Issue
  • - Volume 2013
  • - Article ID 890157
  • - Research Article

Image Denoising via Nonlinear Hybrid Diffusion

Xiaoping Ji | Dazhi Zhang | ... | Boying Wu
  • Special Issue
  • - Volume 2013
  • - Article ID 795651
  • - Research Article

An Implementation Solution for Fractional Partial Differential Equations

Nicolas Bertrand | Jocelyn Sabatier | ... | Jean-Michel Vinassa
  • Special Issue
  • - Volume 2013
  • - Article ID 508543
  • - Research Article

Fast Image Segmentation Based on Efficient Implementation of the Chan-Vese Model with Discrete Gray Level Sets

Songsong Li | Qingpu Zhang
  • Special Issue
  • - Volume 2013
  • - Article ID 569286
  • - Research Article

On a Generalized Laguerre Operational Matrix of Fractional Integration

A. H. Bhrawy | D. Baleanu | ... | J. A. Tenreiro Machado
Mathematical Problems in Engineering
 Journal metrics
See full report
Acceptance rate11%
Submission to final decision118 days
Acceptance to publication28 days
CiteScore2.600
Journal Citation Indicator-
Impact Factor-
 Submit Check your manuscript for errors before submitting

Article of the Year Award: Impactful research contributions of 2022, as selected by our Chief Editors. Discover the winning articles.