Fractional lévy motion and its application to network traffic modeling

Laskin, Nick; Lambadaris, Ioannis; Harmantzis, Fotios C.; Devetsikiotis, Michael

doi:10.1016/s1388-3437(01)80143-8

Cited by 14 publications

(15 citation statements)

References 18 publications

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“…L 2 (R 2 ) is the Fourier operator. From (8), the multiplication operator Aˆ(t) is given byÂ ðtÞ ¼ expðÀðT À tÞð4 2 Þ ð 2 þ 2 Þ Þ, ðA:7Þ withÂ Ã ðtÞ ¼ expðÀðT À tÞð4 2 Þ ð 2 þ 2 Þ Þ: ðA:8Þ Thus,Â À1 ðtÞ ¼ expððT À tÞð4 2 Þ ð 2 þ 2 Þ Þ: ðA:9Þ…”

Section: Concluding Remarkmentioning

confidence: 99%

“…In recent years, fractional calculus and derivative have encountered much success in many fields of science, for instance, mechanical engineering [1][2][3][4][5][6], viscoelasticity [7], Le´vy motion [8], electron transportation [9], dissipation [10], heat conduction [11][12][13], high-frequency financial data [14] and image processing [15][16][17][18]. Hence, in past decades, the study of fractional diffusion equations has attracted intense attention.…”

Section: Introductionmentioning

confidence: 99%

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An optimal method for fractional heat conduction problem backward in time

Xiong

Wang

2012

Applicable Analysis

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In this article, we consider a fractional order backward heat conduction problem in two-dimensional space which is associated with a deblurring problem. The problem is seriously ill-posed. We propose an optimal regularization method to solve the problem in the presence of noisy data, and obtain the optimal stability error estimation. A deblurring and denoising experiment shows that the optimal method is comparable with the Tikhonov method.

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Section: Concluding Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An optimal method for fractional heat conduction problem backward in time

Xiong

Wang

2012

Applicable Analysis

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“…In recent years, fractional calculus and derivatives have encountered big success in modeling problems in many fields of science. For instance, example applications include viscoelastic materials [3,4], network traffic [5], semiconductors [6,7], random-walk models [8,9], and volatility models in finance [10]. In particular, fractional models are believed to be more realistic in describing anomalous diffusion in heterogeneous porous media.…”

Section: Introductionmentioning

confidence: 99%

Regularization for 2-D Fractional Sideways Heat Equations

CaiXian

Ling

Xiong

et al. 2015

Numerical Heat Transfer, Part B: Fundamentals

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In this article, an inverse problem of Caputo-time-fractional sideways heat equations is considered. The aim is to find the inaccessible boundary data of some heterogeneous materials through interior measurements. Instead of the standard Tikhonov approach, we propose a series of fast filters for reconstructing the missing boundary data. Theoretical error bounds are provided for both boundary and (near-boundary) interior reconstructions. Several numerical examples are included to verify the proven convergence results.

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“…[7], the authors constructed generalized fractional Lévy processes as Lévy white noise functionals under a simple condition on Lévy measure. Laskin [11] and Samorodnitsky [17] studied the fractional stable Lévy processes.…”

Section: Introductionmentioning

confidence: 99%