Article
Mathematics, Applied
Abdellatif Ben Makhlouf
Summary: This paper describes the stability analysis of a class of fractional-order nonlinear systems, ensuring the convergence of a part of the solutions towards a ball. By using Lyapunov-like functions, the study examines these nonlinear systems that depend on a small parameter, and guarantees practical stability. Numerical examples are provided to illustrate the validity of the proposed theoretical results, along with a real application to a class of cobweb models.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Automation & Control Systems
Taotao Hu, Zheng He, Xiaojun Zhang, Shouming Zhong, Xueqi Yao
Summary: This paper investigates the delay-dependent stability analysis of fractional-order systems with time-varying delay by proposing novel fractional-order integral inequalities and designing Lyapunov-Krasovskii functions to reduce conservatism, deriving delay-dependent criteria to achieve asymptotic stability of systems with time-varying delay.
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS
(2021)
Article
Physics, Multidisciplinary
D. Vignesh, Naa Fataf, M. F. Abdul Rahim
Summary: This article proposes a fractional order discrete-time neuromuscular model and conducts dynamic analysis, synchronization control, and chemical interpretation to reveal the essential role of the neuromuscular system in information transmission and disease control.
Article
Engineering, Electrical & Electronic
Xiao-Chuang Jin, Jun-Guo Lu
Summary: This brief investigates the master-slave synchronization problem for chaotic fractional-order Lur'e systems. Stability criteria for FO Lur'e systems are established using small gain theorem, and linear output feedback controllers are proposed to asymptotically synchronize chaotic FO Lur'e systems. Numerical examples demonstrate the validity of the proposed results and their less conservative nature compared to existing ones.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
(2021)
Article
Multidisciplinary Sciences
Yu-Ming Chu, Taher Alzahrani, Saima Rashid, Waleed Rashidah, Shafiq Ur Rehman, Mohammad Alkhatib
Summary: This study investigates the impacts of complex interactions on neurological mechanisms using a discrete fractional-order activated nerve cell framework. The findings demonstrate that the influence of fractional-order is dependent on connections between neurons and the system's stored evidence, with implications for surge regularity modification and delays in neural processing.
SCIENTIFIC REPORTS
(2023)
Article
Mathematics, Applied
Yao Xu, Qi Wang, Wenxue Li, Jiqiang Feng
Summary: This paper investigates the stability and synchronization problems of fractional-order delayed multilink complex networks with nonlinear hybrid couplings, considering both discrete time-varying delays and distributed time-varying delays. Criteria are established under feedback control using graph-theoretic approach and Lyapunov method, related to the topological structure of subsystems, control gain, and the upper bound of time-varying delays. The practicality of the results is demonstrated on specific neural networks and chaotic systems, and numerical examples show the effectiveness and feasibility of the theoretical results.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Interdisciplinary Applications
J. L. Echenausia-Monroy, C. A. Rodriguez-Martine, L. J. Ontanon-Garcia, J. Alvarez, J. Pena Ramirez
Summary: This study examines the effectiveness of dynamic coupling as a synchronization strategy for fractional chaotic systems, identifying regions where complete synchronization occurs in the coupled systems. The integration order is considered a key parameter, with statistical metrics and linearized error dynamics used to study the local stability of synchronous solutions. Results show that the integration order affects not only the onset of full synchronization but also the individual dynamic behavior of uncoupled systems.
Article
Mathematics, Interdisciplinary Applications
Prashant M. Gade, Sachin Bhalekar
Summary: This study investigates the stability of linear fractional order maps and finds that the evolution in the stable region is described by Mittag-Leffler functions with a well-defined effective Lyapunov exponent. The research also explores coupled linear fractional maps and stability at fixed points of fractional nonlinear maps, providing insights into the relationship between stability and eigenvalues of coefficient matrices.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2021)
Article
Mathematics
Ardak Kashkynbayev, Fathalla A. Rihan
Summary: This paper investigates the dynamics of a fractional-order epidemic model with general nonlinear incidence rate functionals and time-delay. The study focuses on the local and global stability of steady-states, deducing the basic reproductive threshold parameter. The effectiveness of the theoretical results is illustrated through the consideration of a Holling type III response function in numerical simulations.
Article
Materials Science, Multidisciplinary
M. Ayesha Khatun, Mohammad Asif Arefin, M. Hafiz Uddin, Dumitru Baleanu, M. Ali Akbar, Mustafa Inc
Summary: The article utilizes the fractional modified Riemann-Liouville derivative to study the space-time fractional coupled Boussinesq equation, obtaining multiple mathematical solutions which have significant implications for coastal engineering and the application of nonlinear water wave models.
RESULTS IN PHYSICS
(2021)
Article
Mathematics, Applied
Yumin Dong, Xiang Li, Wei Liao, Dong Hou
Summary: This paper proposes a quantum neural network using multilayer Sigmoid function and learning algorithm to adjust quantum interval, and studies the quasiuniform stability of fractional quantum neural networks with delays. The conditions of quasi uniform stability are given and the sufficiency of the conditions is proved using linear matrix inequality analysis. The feasibility of the conclusion is verified through experiments.
JOURNAL OF FUNCTION SPACES
(2021)
Article
Engineering, Aerospace
Wenjie Qing, Binfeng Pan, Yueyang Hou, Shan Lu, Wenjing Zhang
Summary: In this study, a novel fractional-order sliding mode-based control method was developed for a class of nonautonomous nonlinear systems, using a fractional stability theorem and a fractional-order sliding surface. The applicability and efficiency of the proposed method were demonstrated through simulation results.
Article
Mathematics, Applied
Jiabin Xu, Hassan Khan, Rasool Shah, A. A. Alderremy, Shaban Aly, Dumitru Baleanu
Summary: The research paper presents an efficient technique for solving fractional-order nonlinear Swift-Hohenberg equations related to fluid dynamics, showing that the Laplace Adomian decomposition method requires minimal calculations and produces solutions in close agreement with other existing methods. Numerical examples confirm the validity of the suggested method, demonstrating its almost identical solutions with various analytical methods through graphs and tables.
Article
Engineering, Electrical & Electronic
Yiheng Wei
Summary: The Lyapunov method is a powerful tool for studying the stability of dynamic systems. This paper focuses on the boundedness of nonlinear nabla fractional order systems and derives two stability criteria using the nabla Laplace transform. Two numerical examples are provided to evaluate the effectiveness and practicability of the theoretical results.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS
(2021)
Article
Mathematics, Interdisciplinary Applications
Bo Yan, Fatemeh Parastesh, Shaobo He, Karthikeyan Rajagopal, Sajad Jafari, Matjaz Perc
Summary: This study investigates synchronization in multiplex neuronal networks composed of fractional-order Hindmarsh-Rose neurons and finds that fractional-order models achieve better synchronization compared to integer-order models. By reducing the derivative order of the model, the required coupling strengths for interlayer or intralayer synchronization can be weakened, and the dependence of synchronization on coupling strength decreases.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
