Asymptotically almost periodic solutions for certain differential equations with piecewise constant arguments

Feng, Zonghong; Wang, Yong; Ma, Xin

doi:10.1186/s13662-020-02699-6

Cited by 14 publications

(2 citation statements)

References 56 publications

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“…Yan et al ( 2022 ) revealed a broadband vibration energy harvester based on nonlinear magnetic force and rotary pendulums. Feng et al ( 2020 ) considered the almost periodic solutions for certain differential equations with piecewise constant arguments. Dai et al ( 2014 ) introduced a multi-parameter magnetoelectric response modeling of magnetostrictive laminate.…”

Section: Introductionmentioning

confidence: 99%

A novel fractional discrete grey model with variable weight buffer operator and its applications in renewable energy prediction

et al. 2023

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With the continuous depletion of global fossil energy, optimizing the energy structure has become the focus of attention of all countries. With the support of policy and finance, renewable energy occupies an important position in the energy structure of the USA. Being able to predict the trend of renewable energy consumption in advance plays a vital role in economic development and policymaking. Aiming at the small and changeable annual data of renewable energy consumption in the USA, a fractional delay discrete model of variable weight buffer operator based on grey wolf optimizer is proposed in this paper. Firstly, the variable weight buffer operator method is used to preprocess the data, and then, a new model is constructed by using the discrete modeling method and the concept of fractional delay term. The parameter estimation and time response formula of the new model are deduced, and it is proved that the new model combined with the variable weight buffer operator satisfies the new information priority principle of the final modeling data. The grey wolf optimizer is used to optimize the order of the new model and the weight of the variable weight buffer operator. Based on the renewable energy consumption data of solar energy, total biomass energy and wind energy in the field of renewable energy, the grey prediction model is established. The results show that the model has better prediction accuracy, adaptability and stability than the other five models mentioned in this paper. According to the forecast results, the consumption of solar and wind energy in the USA will increase incrementally in the coming years, while the consumption of biomass will decrease year by year.

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confidence: 99%

A novel fractional discrete grey model with variable weight buffer operator and its applications in renewable energy prediction

et al. 2023

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“…The studies of these kinds of equations were initially mentioned in [20] and [5]. In the following years, qualitative properties such as the stability and convergence [32,34], oscillation [4,8], periodicity [4,6] of solutions of EPCA have been discussed deeply. Although the numerical study of EPCA starts late, it has gradually become more and more popular since EPCA can hardly be solved by analytical methods or much complicated to deal with.…”

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Convergence and Stability of Galerkin Finite Element Method for Hyperbolic Partial Differential Equation With Piecewise Continuous Arguments of Advanced Type

Chen,

Wang

2023

Mathematical Modelling and Analysis

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This paper deals with the convergence and stability of Galerkin finite element method for a hyperbolic partial differential equations with piecewise continuous arguments of advanced type. First of all, we obtain the expression of analytic solution by the method of separation variable, then the sufficient conditions for stability are obtained. Semidiscrete and fully discrete schemes are derived by Galerkin finite element method, and their convergence are both analyzed in L2-norm. Moreover, the stability of the two schemes are investigated. The semidiscrete scheme can achieve unconditionally stability. The sufficient conditions of stability for fully discrete scheme are derived under which the analytic solution is asymptotically stable. Finally, some numerical experiments are presented to illustrate the theoretical results.

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The global Mittag-Leffler synchronization problem of Caputo fractional-order inertial memristive neural networks with time-varying delays

Wang,

2024

Soft Comput

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Asymptotically almost periodic solutions for certain differential equations with piecewise constant arguments

Cited by 14 publications

References 56 publications

A novel fractional discrete grey model with variable weight buffer operator and its applications in renewable energy prediction

A novel fractional discrete grey model with variable weight buffer operator and its applications in renewable energy prediction

Convergence and Stability of Galerkin Finite Element Method for Hyperbolic Partial Differential Equation With Piecewise Continuous Arguments of Advanced Type

The global Mittag-Leffler synchronization problem of Caputo fractional-order inertial memristive neural networks with time-varying delays

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