<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e171" altimg="si463.svg"><mml:mi>S</mml:mi></mml:math>-asymptotically periodic fractional functional differential equations with off-diagonal matrix Mittag-Leffler function kernels

Zhang, Tianwei

doi:10.1016/j.matcom.2021.10.006

Cited by 16 publications

(2 citation statements)

References 23 publications

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“…This section concentrates on some fundamental definitions and properties regarding fractional calculus and the Green function. Please refer to [14,15,[30][31][32] for further details on fractional calculus and more references therein.…”

Section: Fractional Calculus and Green Functionmentioning

confidence: 99%

Three-Point Boundary Value Problems of Coupled Nonlocal Laplacian Equations

Zhou

Zhang

2022

Mathematics

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This paper discusses a kind of coupled nonlocal Laplacian evolution equation with Caputo time-fractional derivatives and proportional delays. Green function and mild solution are firstly established by employing the approach of eigenvalues’ expansions and Fourier analysis technique. By the properties of eigenvalues and Mittag–Leffler functions, several vital estimations of Green functions are presented. In view of these estimations and some appropriate assumptions, the existence and uniqueness of the mild solution are studied by utilizing the Leray–Schauder fixed-point theorem and the Banach fixed-point theorem. Finally, an example is provided to illustrate the effectiveness of our main results.

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Section: Fractional Calculus and Green Functionmentioning

confidence: 99%

Three-Point Boundary Value Problems of Coupled Nonlocal Laplacian Equations

Zhou

Zhang

2022

Mathematics

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“…Therefore, Caputo fractional differential equations were studied by numerous scholars during the last several decades. [17][18][19] On the other hand, the notion of synchronization was originally introduced by Picora and Carroll 20 on behalf of driven-response systems. From then on, different synchronization problems have been widely researched for neural networks and a number of significant findings have been achieved owing to the use of synchronization.…”

Section: Introductionmentioning

confidence: 99%

Equilibrium point, exponential stability and synchronization of numerical fractional-order shunting inhibitory cellular neural networks with piecewise feature

Luo

Zhang

2022

Proceedings of the Institution of Mechanical Engineers, Part I:

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In recent years, exponential Euler difference methods for first-order semi-linear differential equations have been developed rapidly, and various exponential Euler difference methods have become a very important research topic. For fractional-order shunting inhibitory cellular neural networks with time lags, this article first establishes a new difference method named Mittag-Leffler Euler difference, which includes exponential Euler difference. Second, the existence of unique global bounded solution and equilibrium point, exponential stability and synchronization of the derived difference model are investigated. Compared with the classical fractional-order Euler difference method, the Mittag-Leffler discrete shunting inhibitory cellular neural networks can better describe and maintain the dynamic properties of the corresponding continuous-time models. More importantly, it opens up a new way to study discrete-time fractional-order systems and establishes a set of theory and methods to study Mittag-Leffler discrete neural networks.

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Global Exponential Stability and Synchronization of Discrete-Time Fuzzy Bidirectional Associative Memory Neural Networks via Mittag-Leffler Difference Approach

Liu

2023

Int. J. Fuzzy Syst.

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S-asymptotically periodic fractional functional differential equations with off-diagonal matrix Mittag-Leffler function kernels

Cited by 16 publications

References 23 publications

Three-Point Boundary Value Problems of Coupled Nonlocal Laplacian Equations

Three-Point Boundary Value Problems of Coupled Nonlocal Laplacian Equations

Equilibrium point, exponential stability and synchronization of numerical fractional-order shunting inhibitory cellular neural networks with piecewise feature

Global Exponential Stability and Synchronization of Discrete-Time Fuzzy Bidirectional Associative Memory Neural Networks via Mittag-Leffler Difference Approach

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