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Introduction to Fractional Differential Equations pp 87–120Cite as

Generalized Systems

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Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 25))

Abstract

This chapter addresses the generalization of classical models and systems in the perspective of FC. The following sections study the Cornu, Emden, Hermite, Legendre, and Bessel fractional systems.

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Notes

  1. 1.

    M.A. Cornu (1841–1902).

  2. 2.

    H. Müntz (1884–1956).

  3. 3.

    J.P. Gram (1850–1916).

  4. 4.

    J.H. Lane (1819–1880).

  5. 5.

    J.R. Emden (1862–1940).

  6. 6.

    C. Hermite (1822–1901).

  7. 7.

    F. Bessel (1784–1846).

  8. 8.

    A.J. Lotka (1880–1949).

  9. 9.

    E.N. Lorenz (1917–2008).

References

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  3. Johnson, R. S. (2006). The notebook series. the series of second order ordinary differential equation and special function. Technical report, School of Mathematics & Statistics, University of Newcastle upon Tyne.

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  4. Milici, C., & Drăgănescu, G. (2017). Generalization of the equations of Hermite, Legendre and Bessel for the fractional case. Journal of Applied Nonlinear Dynamics, 6, 243–249.

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  5. Milici, C., & Drăgănescu, G. (2017). The Lane-Emden fractional homogenous differential equation. Journal of Applied Nonlinear Dynamics, 6, 237–242.

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  7. Rudin, W. (1966). Fractional calculus with applications for nuclear reactor dynamics. New York: McGraw-Hill.

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  8. von Golitschek, M. (1983). A short proof of Müntz theorem. Journal of Approximation Theory, 39, 394–395.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Polytechnic University of Timişoara, Timişoara, Romania

    Constantin Milici

  2. Research Center in Theoretical Physics, West University of Timişoara, Timişoara, Romania

    Gheorghe Drăgănescu

  3. Department of Electrical Engineering, Polytechnic of Porto, Porto, Portugal

    J. Tenreiro Machado

Authors
  1. Constantin Milici
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  2. Gheorghe Drăgănescu
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  3. J. Tenreiro Machado
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Milici, C., Drăgănescu, G., Tenreiro Machado, J. (2019). Generalized Systems. In: Introduction to Fractional Differential Equations. Nonlinear Systems and Complexity, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-030-00895-6_5

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  • DOI: https://doi.org/10.1007/978-3-030-00895-6_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-00894-9

  • Online ISBN: 978-3-030-00895-6

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