Pharmacokinetic/Pharmacodynamic anesthesia model incorporating psi-Caputo fractional derivatives

Zaitri, Mohamed Abdelaziz; Zitane, Hanaa; Torres, Delfim F.M.

doi:10.1016/j.compbiomed.2023.107679

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Averaging Principle Results1

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2024

2025

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Cited by 8 publications

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“…Take Q = ξ 1 ; when we use Equation (18) in Equation ( 19), and then use (A 1 ) and Jen-Ineq, we obtain the following as a result:…”

Section: Averaging Principle Resultsmentioning

confidence: 99%

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Existence, Uniqueness, and Averaging Principle of Fractional Neutral Stochastic Differential Equations in the Lp Space with the Framework of the Ψ-Caputo Derivative

Mohammed Djaouti,

Khan,

Liaqat

et al. 2024

Mathematics

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In this research work, we use the concepts of contraction mapping to establish the existence and uniqueness results and also study the averaging principle in Lp space by using Jensen’s, Grönwall–Bellman’s, Hölder’s, and Burkholder–Davis–Gundy’s inequalities, and the interval translation technique for a class of fractional neutral stochastic differential equations. We establish the results within the framework of the Ψ-Caputo derivative. We generalize the two situations of p=2 and the Caputo derivative with the findings that we obtain. To help with the understanding of the theoretical results, we provide two applied examples at the end.

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“…Take Q = ξ 1 ; when we use Equation (18) in Equation ( 19), and then use (A 1 ) and Jen-Ineq, we obtain the following as a result:…”

Section: Averaging Principle Resultsmentioning

confidence: 99%

“…In [15], Almeida proposed a novel FrOD concerning a kernel function known as the Ψ-Caputo derivative (Ψ-Cap-D) and extended the results of other academics [16][17][18][19]. They provide a flexible framework for modeling and analyzing complex dynamical systems with memory effects and non-local behaviors.…”

Section: Introductionmentioning

confidence: 99%