Journal of Mathematics

Fractional Operators in Modelling Chaotic and Real-World Problems


Publishing date
01 Jan 2022
Status
Closed
Submission deadline
27 Aug 2021

Lead Editor

1Cheikh Anta Diop University of Dakar, Dakar, Senegal

2Consejo Nacional de Ciencia y Tecnología, Morelos, Mexico

3Federal University of Technology, Akure, Nigeria

This issue is now closed for submissions.
More articles will be published in the near future.

Fractional Operators in Modelling Chaotic and Real-World Problems

This issue is now closed for submissions.
More articles will be published in the near future.

Description

Fractional calculus has become a popular topic for researchers due to its various applications in modelling physical problems, electrical circuits, chaotic systems, diffusion phenomena, epidemical models, etc. Chaotic systems are known to be sensitive to the initial conditions and the variation of the model equations' parameters. Therefore, many tools such as bifurcation maps, Lyapunov exponents, route to chaos, stability, synchronization can be used to analyze dynamics. Chaotic systems have particularly many applications in modelling electrical circuits.

Fractional calculus confirms various fractional operators with the singular kernel as the Caputo derivative and the Riemann-Liouville derivative, and the fractional operators without singular kernels as the Caputo-Fabrizio derivative and the Atangana-Baleanu derivative. There is a need to focus on the impact of the fractional-order operators (new and old) in modelling chaotic systems. Moreover, further research needs to be conducted to analyze how in a fractional context, the fractional chaotic equations can be drawn in terms of electrical circuits. The bifurcation maps and the Lyapunov exponents allow us to characterize types of chaos such as chaotic behaviour and hyperchaotic behaviour when the system's parameters vary in time. The bifurcation and the Lyapunov exponents can also be studied in a fractional context. These two algorithms detecting chaos are complex. However, they should be applicable in a fractional context. The phase portraits of the chaotic systems are also important to observe the real impact of the fractional operator's order in the dynamics of the system. For this reason, numerical algorithms are necessary due to the complexity of the equations.

The aim of this Special Issue is to bring together original research and review articles that will focus on recent advances in modelling fractional-order chaotic systems. Authors are invited to submit their last investigations in modelling chaotic systems or real-word problems with applications in fractional calculus.

Potential topics include but are not limited to the following:

  • Fractional-order chaotic systems
  • Numerical methods for fractional differential equations
  • Numerical schemes for the recent fractional operators
  • Implementation of the fractional chaotic system in modelling electrical circuits
  • Stability and synchronization of the fractional-order chaotic system
  • Recent advances in numerical schemes
  • Mathematical modelling in fractional operators
  • New fractional operators and their numerical discretization
  • Analytical methods for solving fractional differential equations

Articles

  • Special Issue
  • - Volume 2022
  • - Article ID 6989612
  • - Research Article

Conversion of Fructose to 5-Hydroxymethyl Furfural: Mathematical Solution with Experimental Validation

Muhammad Sajid | Apu Chowdhury | ... | Md. Nur Alam
  • Special Issue
  • - Volume 2022
  • - Article ID 5129072
  • - Research Article

The Consensus of Different Fractional-Order Chaotic Multiagent Systems Using Adaptive Protocols

Masoumeh Firouzjahi | Bashir Naderi | Yousef Edrisi Tabriz
  • Special Issue
  • - Volume 2021
  • - Article ID 8231828
  • - Research Article

Analysis of Multiterm Initial Value Problems with Caputo–Fabrizio Derivative

Mohammed Al-Refai | Muhammed Syam
  • Special Issue
  • - Volume 2021
  • - Article ID 1614774
  • - Research Article

A Fractional Epidemiological Model for Bone Remodeling Process

Muath Awadalla | Yves Yannick Yameni Noupoue | Kinda Abuasbeh
  • Special Issue
  • - Volume 2021
  • - Article ID 3320910
  • - Research Article

Research on Population Development Trend in Huizhou of China Forecast Based on Optimal Weighted Combination Method and Fractional Grey Model

Dewang Li | Jianbao Chen | Meilan Qiu
  • Special Issue
  • - Volume 2021
  • - Article ID 6045722
  • - Research Article

On Semianalytical Study of Fractional-Order Kawahara Partial Differential Equation with the Homotopy Perturbation Method

Muhammad Sinan | Kamal Shah | ... | Fathalla Rihan
  • Special Issue
  • - Volume 2021
  • - Article ID 6027246
  • - Research Article

On a Memristor-Based Hyperchaotic Circuit in the Context of Nonlocal and Nonsingular Kernel Fractional Operator

Shahram Rezapour | Chernet Tuge Deressa | Sina Etemad
  • Special Issue
  • - Volume 2021
  • - Article ID 2562227
  • - Research Article

Nonfragile Synchronization of Semi-Markovian Jumping Neural Networks with Time Delays via Sampled-Data Control and Application to Chaotic Systems

K. Sivaranjani | M. Sivakumar | ... | Ngawang Ngmgyel
  • Special Issue
  • - Volume 2021
  • - Article ID 2969717
  • - Research Article

Multiple Positive Solutions for a Class of Boundary Value Problem of Fractional -Difference Equations under -Integral Boundary Conditions

Yongyang Liu | Yansheng Liu
  • Special Issue
  • - Volume 2021
  • - Article ID 3058414
  • - Research Article

Analysis of a Coupled System of Nonlinear Fractional Langevin Equations with Certain Nonlocal and Nonseparated Boundary Conditions

Zaid Laadjal | Qasem M. Al-Mdallal | Fahd Jarad
Journal of Mathematics
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Article of the Year Award: Outstanding research contributions of 2021, as selected by our Chief Editors. Read the winning articles.