Article
Engineering, Multidisciplinary
Hassen Arfaoui, A. Ben Makhlouf, Lassaad Mchiri, Mohamed Rhaima
Summary: In this article, the authors study the Finite-Time Stability (FTS) of Linear Stochastic Fractional Differential Equations of Ito-Doob Type with Delay (LSFDEIDTwD) for a derivative order q E (0, 1). The study investigates the stability of the LSFDEIDTwD in a finite-time domain [0, T] using the generalized Gronwall Inequality (GWI) and stochastic calculus theory. The main results are illustrated with two numerical examples.
ALEXANDRIA ENGINEERING JOURNAL
(2023)
Article
Mathematics, Applied
Lassaad Mchiri, Abdellatif Ben Makhlouf, Dumitru Baleanu, Mohamed Rhaima
Summary: This paper focuses on the finite-time stability of linear stochastic fractional-order systems with time delay for alpha is an element of (1/2, 1). By employing the generalized Gronwall inequality and stochastic analysis techniques, the study investigates the finite-time stability of the solution for linear stochastic fractional-order systems with time delay. Two illustrative examples are provided to demonstrate the significance of the main results.
ADVANCES IN DIFFERENCE EQUATIONS
(2021)
Article
Acoustics
Parvin Mahmoudabadi, Mahsan Tavakoli-Kakhki
Summary: This paper focuses on the stabilization of nonlinear fractional order time-delay systems in the presence of faults. It considers a general class of nonlinear fractional order systems where faults lead to variations in the system dynamics and actuators. The presence of time-varying delays in the system equations is highlighted as important in controlling real-life systems. A precise method, the Takagi-Sugeno fuzzy model, is adopted to facilitate controller design for such systems. New delay-dependent stabilization conditions are established using a Caputo derivative-based Lyapunov-Krasovskii functional in the form of linear matrix inequalities. Two examples, a truck-trailer system and Lorenz system, are simulated to evaluate the research results.
JOURNAL OF VIBRATION AND CONTROL
(2023)
Article
Computer Science, Artificial Intelligence
Feifei Du, Jun-Guo Lu
Summary: This article proposes a new fractional-order Gronwall integral inequality with time delays, which can be widely applied to investigate the finite-time stability of various fractional-order systems. The criteria obtained in this article are less conservative than some existing ones, and the validity of the proposed results is demonstrated through numerical examples.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2021)
Article
Mathematics, Interdisciplinary Applications
Ivanka Stamova, Gani Stamov
Summary: This paper investigates a class of fractional-order delayed impulsive gene regulatory networks, extending existing models using Caputo type fractional derivatives. The study establishes new criteria for the existence and uniqueness of almost periodic states and considers the effects of time-varying delays and impulsive perturbations on the almost periodicity. Additionally, sufficient conditions for global Mittag-Leffler stability of the almost periodic solutions are proposed, with a numerical example provided to support the findings.
FRACTAL AND FRACTIONAL
(2021)
Article
Computer Science, Artificial Intelligence
Mengqi Li, Xujun Yang, Qiankun Song, Xiaofeng Chen
Summary: This paper investigates the Hyers-Ulam stability of fractional-order neural networks with time-varying delays. Several conditions guaranteeing the existence and uniqueness of the exact solution are derived using the successive approximation method and the modified retarded Henry-Gronwall integral inequality. The corresponding results on the Hyers-Ulam-Rassias stability are also provided.
Article
Computer Science, Theory & Methods
Feifei Du, Jun-Guo Lu
Summary: The finite-time stability of fractional-order fuzzy cellular neural networks with time delays is investigated. A new fractional-order Gronwall inequality with time delay is developed for the stability analysis of fractional-order delayed systems. A less conservative criterion for the finite-time stability of fractional-order fuzzy cellular neural networks with time delays is derived based on this inequality. Two examples are given to demonstrate the effectiveness and less conservativeness of the proposed results.
FUZZY SETS AND SYSTEMS
(2022)
Article
Mathematics, Applied
Junqing Jia, Hui Zhang, Huanying Xu, Xiaoyun Jiang
Summary: This paper presents a stabilized second order scheme for the time fractional Allen-Cahn equation, with proven accuracy in time and spectral accuracy in space. A fast evaluation method is developed to save computation time and storage space.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Mathematics, Interdisciplinary Applications
C. Ravichandran, V. Sowbakiya, Kottakkaran Sooppy Nisar
Summary: This paper examines the existence and difference solution of multi-derivative nonlinear fractional integro-differential equations involving the Atangana-Baleanu fractional derivative of Riemann-Liouville sense. The study is based on the T.R. Prabhakar fractional integral operator epsilon(gamma)(sigma, eta, v;c+) and the generalized Mittag-Leffler function. The results are obtained using Krasnoselskii's fixed point theorem and Gronwall-Bellman inequality.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Engineering, Electrical & Electronic
Leipo Liu, Yifan Di, Yilin Shang, Zhumu Fu, Bo Fan
Summary: This paper considers the problem of guaranteed cost and finite-time non-fragile control for a class of fractional-order positive switched systems with asynchronous switching and impulsive moments. Sufficient conditions for system stability are derived via linear programming and specific methods, with controllers designed to ensure system stability and cost constraints. An example of a fractional-order electrical circuit is provided to demonstrate the feasibility and effectiveness of the proposed method.
CIRCUITS SYSTEMS AND SIGNAL PROCESSING
(2021)
Article
Automation & Control Systems
Ticao Jiao, Guangdeng Zong, Ju H. Park, Jian Liu, Yanlei Zhao
Summary: This article addresses the incremental stability problem for stochastic time-varying impulsive and switching systems, providing sufficient criteria to achieve practical incrementally globally asymptotic stability. The feasibility of these results is verified through a numerical example.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2021)
Correction
Mathematics, Applied
William McLean, Kassem Mustapha, Raed Ali, Omar M. Knio
Summary: The note corrects the statement of Theorem 12 from the paper mentioned and fills some gaps in the proof.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2021)
Article
Mathematics, Applied
Veliappan Vijayaraj, Chokkalingam Ravichandran, Thongchai Botmart, Kottakkaran Sooppy Nisar, Kasthurisamy Jothimani
Summary: This article discusses the existence and difference solution of multi-derivative nonlinear neutral fractional order integro-differential equations using specific mathematical operators and functions, and is solved using corresponding theorems and inequalities.
Article
Mathematics, Interdisciplinary Applications
Lili Chen, Minghao Gong, Yanfeng Zhao, Xin Liu
Summary: This paper investigates the finite-time synchronization problem of fractional-order stochastic memristive bidirectional associative memory neural networks (MBAMNNs) with discontinuous jumps. A novel criterion for finite-time synchronization is obtained, providing a new approach to analyze the finite-time synchronization problem of neural networks with stochasticity.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Shasha Wang, Jigui Jian
Summary: This article investigates the predefined-time synchronization of fractional-order memristive competitive neural networks with time-varying delays. Two distinct discontinuous bilayer predefined-time control schemes based on fractional integrals are proposed to address the two-layer structural characteristics of CNNs. By utilizing predefined-time stability theorems and applying fractional-order differential inequalities and other inequality techniques, concise criteria are obtained to ensure the predefined-time stability of two FMCNNs in terms of algebraic inequalities. The predefined time parameter is arbitrary and does not depend on the initial values. Two examples are provided to validate the theoretical results.
CHAOS SOLITONS & FRACTALS
(2023)
