M. De la Sen
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via linear matrix inequalities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Discrete delayed perturbation of Mittag-Leffler function and its application to linear fractional delayed difference system
本文引入常系数线性非齐次分数阶差分系统，通过提出nabla Mittag-Leffler型函数的离散延迟扰动获得显式解，并讨论了相关特殊情况。
In this paper, we propose a delayed perturbation of Mittag-Leffler type matrix function, which is an extension of the classical Mittag-Leffler type matrix function and delayed Mittag-Leffler type matrix function. With the help of the delayed perturbation of Mittag-Leffler type matrix function, we give an explicit formula of solutions to linear nonhomogeneous fractional delay differential equations.
Recovering discrete delayed fractional equations from trajectories
本文提出利用机器学习方法从轨迹中揭示离散动力系统的分数阶与延迟特性，以分数延迟logistic映射为例，证明可检测延迟效应并刻画底层生成模型的分数分量。
This article deals with higher order Caputo fractional variational problems with the presence of delay in the state variables and their integer higher order derivatives.
We propose a delayed Mittag-Leffler type matrix function with logarithm, which is an extension of the classical Mittag-Leffler type matrix function with logarithm and delayed Mittag-Leffler type matrix function. With the help of the delayed Mittag-Leffler type matrix function with logarithm, we give an explicit form a of solutions to nonhomogeneous Hadamard type fractional time-delay linear differential equations. Moreover, we study existence uniqueness and stability in Ulam-Hyers sense of the Hadamard type fractional time-delay nonlinear equations.
The $μ$-neutral linear fractional multi-delayed differential nonhomogeneous system with noncommutative coefficient matrices is introduced. The novel $μ$-neutral multi-delayed perturbation of Mittag-Leffler type matrix function is proposed. Based on this, an explicit solution to the system is investigated step by step. The existence uniqueness of solutions to $μ$-neutral nonlinear fractional multi-delayed differential system is obtained with regard to the supremum norm. The notion of stability analysis in the sense of solutions to the described system is discussed on the grounds of the fixed po…
Finite-time stability of nonlinear conformable fractional-order delayed impulsive systems: Impulsive control and perturbation perspectives
本文基于 conformable 分数阶导数框架，研究了非线性时滞脉冲系统的有限时间稳定性，建立了考虑脉冲控制与扰动的 Lyapunov 判据并估计了稳定时间，最后应用于忆阻神经网络验证有效性。
In this paper, we introduce a delayed Mittag-Leffler type function. With the help of the delayed Mittag-Leffler type functions, we give an explicit formula of solutions to linear nonhomogeneous fractional time-delay Langevin equations involving two Riemann-Liouville fractional derivatives. The existence and uniqueness of solutions are obtained by using an estimation of delayed Mittag-Leffler type functions in terms of exponential functions and a weighted norm via fixed point theorems. Further, we present Ulam--Hyers stability results.
We introduce the delayed Mittag-Leffler type matrix functions, delayed fractional cosine, delayed fractional sine and use the Laplace transform to obtain an analytical solution to the IVP for a Hilfer type fractional linear time-delay system $D_{0,t}^{μ,ν}z\left( t\right) +Az\left( t\right) +Ωz\left( t-h\right) =f\left( t\right) $ of order $1<μ<2$ and type $0\leqν\leq1,$ with nonpermutable matrices $A$ and $Ω$. Moreover, we study Ulam-Hyers stability of the Hilfer type fractional linear time-delay system. Obtained results extend those for Caputo and Riemann-Liouville type fractional linear tim…
Stability criteria of nonlinear generalized proportional fractional delayed systems
针对带时滞的广义比例分数阶系统的有限时间稳定性问题，结合广义比例Grönwall不等式、Mittag-Leffler函数及Hölder、Jensen不等式推导显式判据，并用数值算例验证结果的有效性与可行性。
Harmful information spreading and its impact on vaccination campaigns modeled through fractal-fractional operators
本文利用分形-分数阶算子建模有害信息传播对疫苗接种的影响，并通过Lyapunov函数二阶导数分析疫苗接种动力学中的波动模式。
In this paper, a fractional Lotka-Volterra mathematical model for a bioreactor is proposed and used to fit the data provided by a bioprocess known as continuous fermentation of Zymomonas mobilis. The model contemplates a time-delay $τ$ due to the dead-time in obtaining the measurement of biomass $x(t)$. A Hopf bifurcation analysis is performed to characterize the inherent self oscillatory experimental bioprocess response. As consequence, stability conditions for the equilibrium point together with conditions for limit cycles using the delay $τ$ as bifurcation parameter are obtained. Under the …
This paper is devoted to the investigation of the nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic systems involving delayed dynamics with point delays. The obtained results are independent of the sizes of the delays.
Dynamical Analysis Of Fractional Order Generalized Logistic Map
本研究提出含分数阶与额外参数的广义logistic映射，分析其平衡点稳定性、分岔特性，研究延迟反馈混沌控制、非线性反馈同步及多稳态特性，揭示其更丰富的动力学行为。
Multi-objective LQR with Optimum Weight Selection to Design FOPID Controllers for Delayed Fractional Order Processes
本文提出基于LQR技术的分数阶PID控制器最优折中设计方法，通过两个冲突的时间域控制目标解决有延迟分数阶系统的控制问题，并通过数值模拟验证了两种延迟处理技术的优劣及负载扰动抑制能力。
Fractional Order Sunflower Equation: Stability, Bifurcation and Chaos
本文将向日葵方程推广为含两个分数阶的延迟微分方程，通过线性化稳定性分析给出延迟临界值条件，揭示了稳定、单一稳定区和稳定性切换等分岔现象，并发现多涡卷混沌吸引子。
Stability Analysis of Fractional Difference Equations with Delay
本文推导了带延迟的线性分数阶差分方程的稳定性条件，详细分析了τ=1和τ=2的情形，并将结果扩展到非线性映射。
Stability and Bifurcation Analysis of Two-Term Fractional Differential Equation with Delay
本文针对带时滞的二项分数阶微分方程，通过特征根穿越虚轴的条件进行稳定性与分岔分析，并在参数平面上划分出各类时滞无关和时滞相关的稳定区域。
Delayed Interactions in Active Agents: Stability and Formations
本文建立含惯性与时间延迟的高维线性DDE模型，分析非耦合及对称/非对称耦合主动智能体编队的稳定谱与判据，并证明大延迟极限下稳定区域收敛为以原点为中心的圆。
This paper proves the asymptotic stability of the multidimensional wave equation posed on a bounded open Lipschitz set, coupled with various classes of positive-real impedance boundary conditions, chosen for their physical relevance: time-delayed, standard diffusive (which includes the Riemann-Liouville fractional integral) and extended diffusive (which includes the Caputo fractional derivative). The method of proof consists in formulating an abstract Cauchy problem on an extended state space using a dissipative realization of the impedance operator, be it finite or infinite-dimensional. The a…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。