Fractional Order Bilingualism Model Without Conversion from Dominant Unilingual Group to Bilingual Group

Sofuoglu, Yusuf; Ozalp, Nuri

doi:10.1007/s12591-015-0239-9

Cited by 17 publications

(6 citation statements)

References 10 publications

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“…The most regular definition is the Liouville-Caputo-type definition because the initial condition for fractional order differential equations with Liouville-Caputo-type derivatives is similar in form to the integer-order differential equation [19][20][21][22]. Lemma 1.…”

Section: Fractional Calculusmentioning

confidence: 99%

“…The traditional system of integer-order of differential equations may fail to explain complicated incidents in real phenomena. However, nowadays, fractional order of differential equations has been applied to model the complicated real situations involving many areas-for example, physics, engineering, epidemic, finance and sciences [19][20][21][22][23][24]. The concept of a fractional model helps with expressing the data structure for real life situations more than the integer model.…”

Section: Introductionmentioning

confidence: 99%

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An Analysis on the Fractional Asset Flow Differential Equations

Prathumwan

Sawangtong

2017

Mathematics

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Abstract:The asset flow differential equation (AFDE) is the mathematical model that plays an essential role for planning to predict the financial behavior in the market. In this paper, we introduce the fractional asset flow differential equations (FAFDEs) based on the Liouville-Caputo derivative. We prove the existence and uniqueness of a solution for the FAFDEs. Furthermore, the stability analysis of the model is investigated and the numerical simulation is accordingly performed to support the proposed model.

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Section: Fractional Calculusmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Analysis on the Fractional Asset Flow Differential Equations

Prathumwan

Sawangtong

2017

Mathematics

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“…Fractional differential equations have been successfully used for modeling in finance [7] and epidemiology [8,9], a few examples just to mention. More generally, samples of works in which fractional calculus has successfully been used for modeling are found in [10][11][12][13][14][15][16][17] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Psi-Caputo Logistic Population Growth Model

Awadalla

Noupoue

Abuasbeh

2021

Journal of Mathematics

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This article studies modeling of a population growth by logistic equation when the population carrying capacity K tends to infinity. Results are obtained using fractional calculus theories. A fractional derivative known as psi-Caputo plays a substantial role in the study. We proved existence and uniqueness of the solution to the problem using the psi-Caputo fractional derivative. The Chinese population, whose carrying capacity, K, tends to infinity, is used as evidence to prove that the proposed approach is appropriate and performs better than the usual logistic growth equation for a population with a large carrying capacity. A psi-Caputo logistic model with the kernel function x + 1 performed the best as it minimized the error rate to 3.20% with a fractional order of derivative α = 1.6455.

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“…More recently, ideas from the Baggs-Freedman models have been modified for use as a basis for fractional models of language competition and bilingualism (e.g., [16] ).…”

Section: Introductionmentioning

confidence: 99%

Speaking out: A mathematical model of language preservation

Díaz

Switkes

2021

Heliyon

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Languages evolve as an effect of communal competition while environmental and social dynamics characterize a language. There are thousands of languages spoken around the world but many of them are in danger of going extinct because of language competition and shifts. Modeling language preservation is important because the rise and fall of a language directly impacts the culture attached to it. We present a study of language competition and preservation between a bilingual population and two monolingual populations using a mathematical model involving nonlinear systems of differential equations. Building upon the ideas of previous models in the literature, the model utilizes population proportions with a simple structure that yields noteworthy behavior including a stable spiral with all three language groups preserved. We investigate how bilinguals and monolinguals can coexist as well as how they can affect one another. Los idiomas evolucionan como efecto de la competencia comunitaria, mientras que las dinámicas ambientales y sociales caracterizan a un idioma. Se hablan miles de idiomas en todo el mundo, pero muchos de ellos están en peligro de extinción debido a la competencia lingüística y los cambios. Modelar la preservación del lenguaje es importante porque el auge y la caída de un idioma impacta directamente en la cultura que se le atribuye. Presentamos un estudio de la competencia y preservación del lenguaje entre una población bilingüe y dos poblaciones monolingües utilizando un modelo matemático que involucra sistemas no lineales de ecuaciones diferenciales. Sobre la base de las ideas de modelos anteriores en la literatura, el modelo utiliza proporciones de población con una estructura simple que produce un comportamiento notable que incluye una espiral estable con los tres grupos lingüísticos preservados. Investigamos cómo los bilingües y los monolingües pueden coexistir y cómo pueden afectarse unos a otros.

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Fractional Order Bilingualism Model Without Conversion from Dominant Unilingual Group to Bilingual Group

Cited by 17 publications

References 10 publications

An Analysis on the Fractional Asset Flow Differential Equations

An Analysis on the Fractional Asset Flow Differential Equations

Psi-Caputo Logistic Population Growth Model

Speaking out: A mathematical model of language preservation

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