Existence and controllability for conformable fractional stochastic differential equations with infinite delay via measures of noncompactness

Huang, Jizhao; Luo, Danfeng

doi:10.1063/5.0125651

Cited by 16 publications

(5 citation statements)

References 37 publications

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“…Recently, in the work of Li et al [22], by means of delayed matrix functions of M-L, the researchers sought the representation of solution and presented controllability of the linear FDDEs. For more detail about controllability, we can pay attention to previous works [23][24][25][26][27][28][29][30].…”

Section: Previous Workmentioning

confidence: 99%

Relatively exact controllability of fractional stochastic delay system driven by Lévy noise

Huang

Luo

2023

Math Methods in App Sciences

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In this article, we consider the relatively exact controllability of fractional stochastic delay system (FSDS) driven by Lévy noise. First, we derive the solution of linear FSDS via delayed matrix functions of Mittag-Leffler (M-L). Subsequently, by virtue of the controllability Grammian matrix, we explore the relatively exact controllability of linear FSDS. In addition, with the aid of Jensen's inequality, Hölder's inequality, and Itô's isometry, the existence and uniqueness of the considered nonlinear FSDS are investigated by employing Banach contraction principle. Thereafter, the relatively exact controllability of nonlinear FSDS is discussed. Finally, the theoretical results are supported through examples.

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Section: Previous Workmentioning

confidence: 99%

Relatively exact controllability of fractional stochastic delay system driven by Lévy noise

Huang

Luo

2023

Math Methods in App Sciences

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“…In theoretical research, fractional calculus also can be applied in stability theory [1][2][3], control theory [4,5] and stochastic analysis [6,7]. For have a more effective illustration, one can pay attention to refer the monographs [8][9][10][11] and previous studies [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Relatively exact controllability of fractional stochastic neutral system with two incommensurate constant delays

Yuan,

Luo

2024

Math Methods in App Sciences

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This paper is devoted to analyzing a kind of fractional stochastic neutral system (FSNS). Firstly, by introducing the notion of newly defined two‐parameter Mittag–Leffler matrix function, we derive the solution of the corresponding linear stochastic system. Subsequently, for the linear case, by virtue of the Grammian matrix, we give a suffcient and necessary condition to guarantee the relatively exact controllability for the addressed case. Furthermore, for the nonlinear one, the relatively exact controllability is obtained by fixed point and explore it via Banach contraction principle. Finally, two examples are provided to intensify our theoretical conclusions.

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“…Proper temporal coordination requires synchronization of tissue-specific rhythms, which in turn requires synchronization of cell-level clocks. Loss of synchrony between organ systems and dampening of circadian rhythms has been implicated in aging and disease [6]. In older mice, for example, it has been reported that the flattened amplitude of circadian oscillation is related to deficits in long-term spatial memory due to impaired sleep [7].…”

Section: Introductionmentioning

confidence: 99%

Detecting Rhythmic Gene Expression in Single Cell Transcriptomics

Xu,

Ma,

Abruzzi

et al. 2023

Preprint

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An autonomous, environmentally-synchronizable circadian rhythm is a ubiquitous feature of life on Earth. In multicellular organisms, this rhythm is generated by a transcription–translation feedback loop present in nearly every cell that drives daily expression of thousands of genes in a tissue–dependent manner. Identifying the genes that are under circadian control can elucidate the mechanisms by which physiological processes are coordinated in multicellular organisms. Today, transcriptomic profiling at the single-cell level provides an unprecedented opportunity to understand the function of cell-level clocks. However, while many cycling detection algorithms have been developed to identify genes under circadian control in bulk transcriptomic data, it is not known how best to adapt these algorithms to single-cell RNAseq data. Here, we benchmark commonly used circadian detection methods on their reliability and efficiency when applied to single cell RNAseq data. Our results provide guidance on adapting existing cycling detection methods to the single-cell domain, and elucidate opportunities for more robust and efficient rhythm detection in single-cell data. We also propose a subsampling procedure combined with harmonic regression as an efficient, reliable strategy to detect circadian genes in the single–cell setting.

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Existence and controllability for conformable fractional stochastic differential equations with infinite delay via measures of noncompactness

Cited by 16 publications

References 37 publications

Relatively exact controllability of fractional stochastic delay system driven by Lévy noise

Relatively exact controllability of fractional stochastic delay system driven by Lévy noise

Relatively exact controllability of fractional stochastic neutral system with two incommensurate constant delays

Detecting Rhythmic Gene Expression in Single Cell Transcriptomics

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