Semigroup property of fractional differential operators and its applications

Cong, Nguyen Dinh

doi:10.3934/dcdsb.2022064

Cited by 3 publications

(2 citation statements)

References 7 publications

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“…To resolve this problem, we considered a latent variable z such that z is defined as z ¼ D 1À a t y. Generally, the Caputo derivative dose not satisfy a semigroup property with respect to α of differentiation; however, it possesses a semigroup property under some additional assumptions [19,20], which are D 1 t yðtÞ and D 1À a t ðD a t yðtÞÞ are continuous on R. Then semigroup property y 0 ðtÞ ¼ D 1 t yðtÞ ¼ D a t ðD 1À a yÞ is satisfied. The system given by Eq ( 4) is transformed into a multi-order system of fractionalorder equations and computer simulation such as fde12 can be used.…”

Section: System Modification For Implementation: Semigroup Propertymentioning

confidence: 99%

“…To compare them, the simulation of the fractional TCM is carefully considered because fractional TCM has a system of equations with a mixture of ordinary and fractional derivatives in an equation. The property of semigroup of a fractional derivative is applied to the model under some conditions to resolve this challenge [19,20]. Subsequently, model robustness and sensitivity analysis were investigated for model validation.…”

Section: Introductionmentioning

confidence: 99%

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Fractional transit compartment model for describing drug delayed response to tumors using Mittag-Leffler distribution on age-structured PKPD model

et al. 2022

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The response of a cell population is often delayed relative to drug injection, and individual cells in a population of cells have a specific age distribution. The application of transit compartment models (TCMs) is a common approach for describing this delay. In this paper, we propose a TCM in which damaged cells caused by a drug are given by a single fractional derivative equation. This model describes the delay as a single equation composed of fractional and ordinary derivatives, instead of a system of ODEs expressed in multiple compartments, applicable to the use of the PK concentration in the model. This model tunes the number of compartments in the existing model and expresses the delay in detail by estimating an appropriate fractional order. We perform model robustness, sensitivity analysis, and change of parameters based on the amount of data. Additionally, we resolve the difficulty in parameter estimation and model simulation using a semigroup property, consisting of a system with a mixture of fractional and ordinary derivatives. This model provides an alternative way to express the delays by estimating an appropriate fractional order without determining the pre-specified number of compartments.

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Section: System Modification For Implementation: Semigroup Propertymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fractional transit compartment model for describing drug delayed response to tumors using Mittag-Leffler distribution on age-structured PKPD model

et al. 2022

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A constructive approach for investigating the stability of incommensurate fractional differential systems

Diethelm,

Hashemishahraki,

Thai

et al. 2024

Journal of Mathematical Analysis and Applications

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Tychonoff Solutions of the Time-Fractional Heat Equation

Ascione

2022

Fractal Fract

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In the literature, one can find several applications of the time-fractional heat equation, particularly in the context of time-changed stochastic processes. Stochastic representation results for such an equation can be used to provide a Monte Carlo simulation method, upon proving that the solution is actually unique. In the classical case, however, this is not true if we do not consider any additional assumption, showing, thus, that the Monte Carlo simulation method identifies only a particular solution. In this paper, we consider the problem of the uniqueness of the solutions of the time-fractional heat equation with initial data. Precisely, under suitable assumptions about the regularity of the initial datum, we prove that such an equation admits an infinity of classical solutions. The proof mimics the construction of the Tychonoff solutions of the classical heat equation. As a consequence, one has to add some addtional conditions to the time-fractional Cauchy problem to ensure the uniqueness of the solution.

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Semigroup property of fractional differential operators and its applications

Cited by 3 publications

References 7 publications

Fractional transit compartment model for describing drug delayed response to tumors using Mittag-Leffler distribution on age-structured PKPD model

Fractional transit compartment model for describing drug delayed response to tumors using Mittag-Leffler distribution on age-structured PKPD model

A constructive approach for investigating the stability of incommensurate fractional differential systems

Tychonoff Solutions of the Time-Fractional Heat Equation

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