Mathematical modeling in selected biological systems with fractional Brownian motion

Filatova, Darya; Grzywaczewski, M.

doi:10.1109/hsi.2008.4581546

Cited by 2 publications

(2 citation statements)

References 14 publications

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“…Especially, by using the fractional Brownian motion (fBm) the handled deterministic model can be transformed to the Stochastic Differential Equation (SDE). Hereby, it can give us more flexibility to describe the complexity and randomness of biological systems [9,4,27]. Furthermore, the e-cigarette smoking…”

Section: Discussionmentioning

confidence: 99%

Investigation of E-Cigarette Smoking Model with Mittag-Leffler Kernel

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Evirgen

et al. 2021

Foundations of Computing and Decision Sciences

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Smoking is the most lethal social poisoning event. The World Health Organization defines smoking as the most important preventable cause of disease. Around 4.9 million people worldwide die from smoking every year. In order to analysis this matter, we aim to investigate an e-cigarette smoking model with Atangana-Baleanu fractional derivative. We obtain the existence conditions of the solution for this fractional model utilizing fixed-point theory. After giving existence conditions, the uniqueness of the solution is proved. Finally, to show the effect of the Atangana-Baleanu fractional derivative on the model, we give some numerical results supported by illustrative graphics.

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Section: Discussionmentioning

confidence: 99%

Investigation of E-Cigarette Smoking Model with Mittag-Leffler Kernel

Uçar

Evirgen

et al. 2021

Foundations of Computing and Decision Sciences

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“…However, the observer design issues on a linear system with stochastic noised disturbances are still a challenge. Especially, for the applications such as systems biology [12] and/or vehicular electronics [2], the disturbance may appeal in a probability model that deteriorate the performance of state estimation in the observer mechanism. In order to investigate these phenomena, this study considers applying the Brownian motions to sketch the noised disturbing model.…”

Section: Introductionmentioning

confidence: 99%

Detection of Stochastic Noise in Vehicular Applications

2012

2012 IEEE 75th Vehicular Technology Conference (VTC Spring)

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This paper considers observer design and controllability issues on vehicular systems with stochastic noises. The noised disturbances are modeled as independent Brownian motions for affections such as radiation, heat and material fatigue. Under this framework, this paper proposes the design and controllability conditions on a Proportional-Integral observer in terms of four crucial theorems. The results can be applied to state and disturbance estimations in related applications.

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Mathematical modeling in selected biological systems with fractional Brownian motion

Cited by 2 publications

References 14 publications

Investigation of E-Cigarette Smoking Model with Mittag-Leffler Kernel

Investigation of E-Cigarette Smoking Model with Mittag-Leffler Kernel

Detection of Stochastic Noise in Vehicular Applications

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