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

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Abstract

A fractional order model of a population with one bilingual and two unilingual components, in which conversion from dominant unilingual to bilingual doesn’t exist is studied. Equilibrium points are found, criteria for the existence and the stability of the positive equilibrium are then investigated. Also, numerical solutions for an example of the fractional order system are obtained by transforming the fractional system to the corresponding integer order one.

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References

  1. Baggs, I., Freedman, H.I.: Can the speakers of dominated language survive as unilinguals?: A mathematical model on bilingualism. J. Mat. Comput. Model. 18(6), 9–18 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  2. Paul, M., Simons, G.F., Fennig, C.D. (eds.): Ethnologue: Languages of the world, 17th edn. SIL International, Dallas (2013)

  3. Baggs, I., Freedman, H.I.: A mathematical model for the dynamical interactions between a unilingual and bilingual population: persistence versus extinction. J. Math. Sociol. 16, 51–75 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  4. El-Owaidy, H.M., Ismail, M.: A mathematical model on bilingualism. Appl. Math. Comput. 131, 415–432 (2002)

    MathSciNet  MATH  Google Scholar 

  5. Sree Hari Rao, V., Raja Sekhara Rao, P.: Dynamical models for the development of unilingual society into bilingual society. Differ. Equat. Dyn. Syst. 16, 29–45 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Wyburn, J., Hayward, J.: The future of bilingualism: an application of the Baggs and Freedman model. J. Math. Sociol. 32, 267–284 (2008)

    Article  MATH  Google Scholar 

  7. Özalp, N., Demirci, E.: A fractional order SEIR model with vertical transmission. Math. Comput. Model. 54, 1–6 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Diethelm, K.: The Analysis of Fractional Dfferential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type, In: Lecture Notes in Mathematics. Springer-Verlag, Berlin (2010)

    MATH  Google Scholar 

  9. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)

    MATH  Google Scholar 

  10. Tenreiro Machado, J.: Numerical analysis of the initial conditions in fractional systems. Commun. Nonlinear Sci. Numer. Simulat. 19, 2935–2941 (2014)

    Article  MathSciNet  Google Scholar 

  11. Demirci, E., Özalp, N.: A method for solving differential equations of fractional order. J. Comput. Appl. Math. 236, 2754–2762 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  12. Ahmed, E., El-Sayed, A.M.A., El-Saka, H.A.A.: Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models. J. Math. Anal. Appl. 325, 542–553 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  13. Matignon, D.: Stability results for fractional differential equations with applications to control processing. Comput. Eng. Syst. Appl. 2, 963 (1996)

    Google Scholar 

  14. Ahmed, E., El-Sayed, A.M.A., El-Saka, H.A.A.: On some Routh–Hurwitz conditions for fractional differential equations and their applications in Lorenz, Rössler, Chua and Chen systems. Phys. Lett. A 358, 1–4 (2006)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Ankara University, Besevler, 06100, Ankara, Turkey

    Y. Sofuoglu & N. Ozalp

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  1. Y. Sofuoglu
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  2. N. Ozalp
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Correspondence to Y. Sofuoglu.

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Sofuoglu, Y., Ozalp, N. Fractional Order Bilingualism Model Without Conversion from Dominant Unilingual Group to Bilingual Group. Differ Equ Dyn Syst 25, 1–9 (2017). https://doi.org/10.1007/s12591-015-0239-9

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