Averaging principle for fractional stochastic differential equations with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e82" altimg="si6.svg"><mml:msup><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msup></mml:math> convergence

Wang, Zhaoyang; Lin, Ping

doi:10.1016/j.aml.2022.108024

Cited by 12 publications

(9 citation statements)

References 8 publications

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“…Remark 1. If ψ(t) ≡ t, g ≡ 0, and τ = 0, then FSDDEs (3) reduces to FSDEs (1) in [18]. Therefore, Theorem 1 generalizes the main result of [18].…”

Section: Resultsmentioning

confidence: 54%

“…(iii) Our work in this paper is novel and more technical. Our result has greatly promoted and extended the main result of [18]. This paper will be organized as follows.…”

Section: Introductionmentioning

confidence: 72%

“…Recently, Wang and Lin [18] extended the averaging principle of the following fractional stochastic differential equations (FSDEs)…”

Section: Introductionmentioning

confidence: 99%

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Averaging Principle for ψ-Capuo Fractional Stochastic Delay Differential Equations with Poisson Jumps

2023

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In this paper, we study the averaging principle for ψ-Capuo fractional stochastic delay differential equations (FSDDEs) with Poisson jumps. Based on fractional calculus, Burkholder-Davis-Gundy’s inequality, Doob’s martingale inequality, and the Ho¨lder inequality, we prove that the solution of the averaged FSDDEs converges to that of the standard FSDDEs in the sense of Lp. Our result extends some known results in the literature. Finally, an example and simulation is performed to show the effectiveness of our result.

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“…Remark 1. If ψ(t) ≡ t, g ≡ 0, and τ = 0, then FSDDEs (3) reduces to FSDEs (1) in [18]. Therefore, Theorem 1 generalizes the main result of [18].…”

Section: Resultsmentioning

confidence: 54%

“…(iii) Our work in this paper is novel and more technical. Our result has greatly promoted and extended the main result of [18]. This paper will be organized as follows.…”

Section: Introductionmentioning

confidence: 72%

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Averaging Principle for ψ-Capuo Fractional Stochastic Delay Differential Equations with Poisson Jumps

2023

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“…Additionally, Luo et al [53] studied the average principle of delay FSDEs, focusing on the L 2 space. Moreover, Wang et al [54] established the result of the average principle for FNSDEs in the pth moment. For further details regarding the averaging approach, see [55][56][57][58][59][60][61][62][63].…”

mentioning

confidence: 99%

“…We generalized the result of the averaging principle established in the context of CFD [54] by employing CKFD. We attained the result [54] by setting ℓ = 1 in our established result.…”

mentioning

confidence: 99%

A Study of Some Generalized Results of Neutral Stochastic Differential Equations in the Framework of Caputo–Katugampola Fractional Derivatives

Mohammed Djaouti,

Khan,

Imran Liaqat

et al. 2024

Mathematics

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Inequalities serve as fundamental tools for analyzing various important concepts in stochastic differential problems. In this study, we present results on the existence, uniqueness, and averaging principle for fractional neutral stochastic differential equations. We utilize Jensen, Burkholder–Davis–Gundy, Grönwall–Bellman, Hölder, and Chebyshev–Markov inequalities. We generalize results in two ways: first, by extending the existing result for p=2 to results in the Lp space; second, by incorporating the Caputo–Katugampola fractional derivatives, we extend the results established with Caputo fractional derivatives. Additionally, we provide examples to enhance the understanding of the theoretical results we establish.

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Some New Results on Itô–Doob Hadamard Fractional Stochastic Pantograph Equations in $$L^p$$ Spaces

Zhang,

2024

Qual. Theory Dyn. Syst.

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Averaging principle for fractional stochastic differential equations with Lp convergence

Cited by 12 publications

References 8 publications

Averaging Principle for ψ-Capuo Fractional Stochastic Delay Differential Equations with Poisson Jumps

Averaging Principle for ψ-Capuo Fractional Stochastic Delay Differential Equations with Poisson Jumps

A Study of Some Generalized Results of Neutral Stochastic Differential Equations in the Framework of Caputo–Katugampola Fractional Derivatives

Some New Results on Itô–Doob Hadamard Fractional Stochastic Pantograph Equations in $$L^p$$ Spaces

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