Discrete Dynamics in Nature and Society

Discrete Dynamics of Fractional Systems: Theory and Numerical Techniques


Publishing date
16 Feb 2018
Status
Published
Submission deadline
29 Sep 2017

1Universidad Autónoma de Aguascalientes, Aguascalientes, Mexico

2Baylor University, Waco, USA

3University of Salerno, Fisciano, Italy


Discrete Dynamics of Fractional Systems: Theory and Numerical Techniques

Description

In recent decades, fractional calculus has found a large number of profound applications, which have triggered the development of both the theory and methods for more reliable discretization and approximations of the dynamics of continuous systems. Fractional order models and discrete problems are nonlocal. They provide better descriptions and, ultimately, a better understanding of underlying complex phenomena in sciences and technology. To that end, novel analytical methods to investigate qualitative features of the solutions of these nonlocal systems as well as more general results on the existence and the uniqueness of suitable solutions are desirable tools in the study of fractional systems.

At the same time, continuous models based on systems of ordinary or partial differential equations have been investigated via various criteria of discretization. Novel numerical methods to approximate the solutions of fractional systems have emerged in the literature. However, the search for discrete techniques which are faster and stable, which possess a higher order of convergence at lower computational costs, and which preserve the main features of the solutions of interest, is a constant pursuit in the numerical analysis. In particular, the design of discretization of continuous fractional systems that preserve important characteristics, such as positivity, boundedness, convexity, monotonicity, and energy, is a fruitful area of research that merits a closer attention.

In light of these facts, the purpose of this special issue is to publish original high-quality research papers and review articles that address the latest progress on theoretical analytical methods of discrete fractional systems or that analyze new numerical discretization of fractional differential equations arising in the sciences and technology. Rather than mere applications of standard analytical and numerical techniques, our emphasis is on novel theoretical results and the analysis of new methodologies.

Potential topics include but are not limited to the following:

  • Innovative methods of theoretical analysis
  • Existence and uniqueness of solutions
  • Structure-preserving discretization
  • Qualitative properties of fractional equations and systems
  • Novel approximations of nonlocal fractional problems
  • Applications of fractional systems to relevant topics in nature and society

Articles

  • Special Issue
  • - Volume 2018
  • - Article ID 1079748
  • - Editorial

Discrete Dynamics of Fractional Systems: Theory and Numerical Techniques

Jorge E. Macías-Díaz | Qin Sheng | Stefania Tomasiello
  • Special Issue
  • - Volume 2018
  • - Article ID 5157267
  • - Research Article

Lebesgue-p Norm Convergence Analysis of PDα-Type Iterative Learning Control for Fractional-Order Nonlinear Systems

Lei Li
  • Special Issue
  • - Volume 2018
  • - Article ID 5268528
  • - Research Article

Existence Results of Initial Value Problems for Hybrid Fractional Sum-Difference Equations

Saowaluck Chasreechai | Thanin Sitthiwirattham
  • Special Issue
  • - Volume 2017
  • - Article ID 3540364
  • - Research Article

Homotopy Series Solutions to Time-Space Fractional Coupled Systems

Jin Zhang | Ming Cai | ... | Hui Wei
  • Special Issue
  • - Volume 2017
  • - Article ID 2658124
  • - Research Article

Numerical Simulation of One-Dimensional Fractional Nonsteady Heat Transfer Model Based on the Second Kind Chebyshev Wavelet

Fuqiang Zhao | Jiaquan Xie | Qingxue Huang
  • Special Issue
  • - Volume 2017
  • - Article ID 4057089
  • - Research Article

Numerical Analysis of Fractional Order Epidemic Model of Childhood Diseases

Fazal Haq | Muhammad Shahzad | ... | Ghaus ur Rahman
  • Special Issue
  • - Volume 2017
  • - Article ID 8607946
  • - Research Article

Weak Solutions for Partial Random Hadamard Fractional Integral Equations with Multiple Delays

Saïd Abbas | Mouffak Benchohra | ... | Ahmed Alsaedi
  • Special Issue
  • - Volume 2017
  • - Article ID 2049396
  • - Research Article

Modified Function Projective Synchronization for a Partially Linear and Fractional-Order Financial Chaotic System with Uncertain Parameters

Yehong Yang | Guohua Cao
  • Special Issue
  • - Volume 2017
  • - Article ID 1586249
  • - Research Article

Two New Approximations for Variable-Order Fractional Derivatives

Ruilian Du | Zongqi Liang
Discrete Dynamics in Nature and Society
 Journal metrics
Acceptance rate24%
Submission to final decision59 days
Acceptance to publication84 days
CiteScore0.990
Impact Factor0.973
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