Strong convergence of a fractional exponential integrator scheme for finite element discretization of time-fractional SPDE driven by fractional and standard Brownian motions

Noupelah, Aurelien Junior; Tambue, Antoine; Woukeng, Jean Louis

doi:10.1016/j.cnsns.2023.107371

Cited by 2 publications

(1 citation statement)

References 21 publications

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“…In 2023, Noupelah et al [52] studied the strong convergence of a numerical approximation method for a general time-fractional SPDE defined on a bounded domain Λ ⊂ R d (d = 1, 2, 3) with a smooth boundary. Such a model is pertinent for modeling random phenomena affecting particle transport in media with thermal memory, that is…”

Section: Chronological Progression Of Numerical Methods For Fspdesmentioning

confidence: 99%

Fractional Stochastic Partial Differential Equations: Numerical Advances and Practical Applications—A State of the Art Review

Moghaddam,

Babaei,

Dabiri

et al. 2024

Symmetry

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This article aims to provide a comprehensive review of the latest advancements in numerical methods and practical implementations in the field of fractional stochastic partial differential equations (FSPDEs). This type of equation integrates fractional calculus, stochastic processes, and differential equations to model complex dynamical systems characterized by memory and randomness. It introduces the foundational concepts and definitions essential for understanding FSPDEs, followed by a comprehensive review of the diverse numerical methods and analytical techniques developed to tackle these equations. Then, this article highlights the significant expansion in numerical methods, such as spectral and finite element methods, aimed at solving FSPDEs, underscoring their potential for innovative applications across various disciplines.

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Section: Chronological Progression Of Numerical Methods For Fspdesmentioning

confidence: 99%

Fractional Stochastic Partial Differential Equations: Numerical Advances and Practical Applications—A State of the Art Review

Moghaddam,

Babaei,

Dabiri

et al. 2024

Symmetry

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show abstract

PSD and Cross-PSD of Responses of Seven Classes of Fractional Vibrations Driven by fGn, fBm, Fractional OU Process, and von Kármán Process

2024

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This paper gives its contributions in four stages. First, we propose the analytical expressions of power spectrum density (PSD) responses and cross-PSD responses to seven classes of fractional vibrators driven by fractional Gaussian noise (fGn). Second, we put forward the analytical expressions of PSD and cross-PSD responses to seven classes of fractional vibrators excited by fractional Brownian motion (fBm). Third, we present the analytical expressions of PSD and cross-PSD responses to seven classes of fractional vibrators driven by the fractional Ornstein–Uhlenbeck (OU) process. Fourth, we bring forward the analytical expressions of PSD and cross-PSD responses to seven classes of fractional vibrators excited by the von Kármán process. We show that the statistical dependences of the responses to seven classes of fractional vibrators follow those of the excitation of fGn, fBm, the OU process, or the von Kármán process. We also demonstrate the obvious effects of fractional orders on the responses to seven classes of fractional vibrations. In addition, we newly introduce class VII fractional vibrators, their frequency transfer function, and their impulse response in this research.

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Strong convergence of a fractional exponential integrator scheme for finite element discretization of time-fractional SPDE driven by fractional and standard Brownian motions

Cited by 2 publications

References 21 publications

Fractional Stochastic Partial Differential Equations: Numerical Advances and Practical Applications—A State of the Art Review

Fractional Stochastic Partial Differential Equations: Numerical Advances and Practical Applications—A State of the Art Review

PSD and Cross-PSD of Responses of Seven Classes of Fractional Vibrations Driven by fGn, fBm, Fractional OU Process, and von Kármán Process

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