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A Numerical Method for Solution of Ordinary Differential Equations of Fractional Order

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Parallel Processing and Applied Mathematics (PPAM 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2328))

Abstract

In this paper we propose an algorithm for the numerical solution of arbitrary differential equations of fractional order. The algorithm is obtained by using the following decomposition of the differential equation into a system of differential equation of integer order connected with inverse forms of Abel-integral equations. The algorithm is used for solution of the linear and non-linear equations.

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References

  1. Babenko Yu. I.: Heat and Mass Transfer, Khimiya, Leningrad (1986) (in Russian)

    Google Scholar 

  2. Blank L.: Numerical Treatment of Differential Equations of Fractional Order, Numerical Analysis Report 287, Manchester Centre for Computational Mathematics, Menchester (1996), pp. 1–16

    Google Scholar 

  3. Carpinteri A. and Mainardi F. (eds.): Fractals and Fractional Calculus in Continuum Mechanics, Springer Verlag, Vienna-New-York, (1997)

    MATH  Google Scholar 

  4. Diethelm K.: An algorithm for the numerical solution of differential equations of fractional order, Elec. Transact. Numer. Anal. 5 (1997), pp. 1–6

    MathSciNet  MATH  Google Scholar 

  5. Goto M. and Oldham K.B.: Semiintegral electroanalysis: shapes of the neopolaro-geographic plateau, Anal. Chem., 61, (1975), pp. 361–365

    Google Scholar 

  6. Konguetsof A. and Simons T.E.: On the construction of exponentially fitted methods for the numerical solution of the Schrodinger equation, Journal of Computational Methods in Sciences and Engineering, 1, (2001), pp. 143–160

    MATH  Google Scholar 

  7. Oldham K. B. and Spanier J.: The fractional Calculus, Academic Press, New York and London (1974)

    MATH  Google Scholar 

  8. Palczewski A.: Ordinary differential equations, WNT, Warsaw (1999) (in Polish)

    Google Scholar 

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

    MATH  Google Scholar 

  10. Riewe F.: Nonconservative Lagrangian and Hamiltonian mechanics, Phys. Rev. E 53(2) (1996) pp. 1890–1899

    Article  MathSciNet  Google Scholar 

  11. Riewe F.: Mechanics with fractional derivatives, Phys. Rev. E 55(3) (1997), pp. 3581–3592

    Article  MathSciNet  Google Scholar 

  12. Samko S. G., Kilbas A. A. i Marichev O. I.: Integrals and derivatives of fractional order and same of their applications, Gordon and Breach, London (1993)

    Google Scholar 

  13. Simons T.E.: On finite difference methods for the solution of the Schrodinger equation, Computers & Chemistry 23 (1999), pp. 513–555

    Article  Google Scholar 

  14. Simons T.E.: Atomic structure computations in chemical modelling: Applications and theory (Ed.: A. Hinchliffe, UMIST) The Royal Society of Chemistry, (2000), pp. 38–142

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Mathematics & Computer Science, Technical University of Częstochowa, ul. Dabrowskiego 73, 42-200, Częstochowa, Poland

    Jacek Leszczyński & Mariusz Ciesielski

Authors
  1. Jacek Leszczyński
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  2. Mariusz Ciesielski
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Editor information

Editors and Affiliations

  1. Institute of Mathematics and Computer Science, Technical University of Czestochowa, Dabrowskiego 73, 42-200, Czestochowa, Poland

    Roman Wyrzykowski

  2. Computer Science Department, University of Tennessee, 122 Volunteer Blvd, Knoxville, TN, 37996-3450, USA

    Jack Dongarra

  3. Computer Science Department, Oklahoma State University, 700 N. Greenwood Ave., Tulsa, OK, 74106, USA

    Marcin Paprzycki

  4. DTU, UNI-C, Danish Computing Centre for Research and Education, Bldg. 304, 2800, Lyngby, Denmark

    Jerzy Waśniewski

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© 2002 Springer-Verlag Berlin Heidelberg

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Leszczyński, J., Ciesielski, M. (2002). A Numerical Method for Solution of Ordinary Differential Equations of Fractional Order. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2001. Lecture Notes in Computer Science, vol 2328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48086-2_77

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  • DOI: https://doi.org/10.1007/3-540-48086-2_77

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43792-5

  • Online ISBN: 978-3-540-48086-0

  • eBook Packages: Springer Book Archive

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