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Advances in the Theory and Applications of Non-integer Order Systems pp 161–170Cite as

Exact Solution of Two-Term Nonlinear Fractional Differential Equation with Sequential Riemann-Liouville Derivatives

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Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 257))

Abstract

In this paper we derive a general solution for a class of nonlinear sequential fractional differential equations (SFDEs) with Riemann -Liouville (R-L) derivatives of arbitrary order. The solution of such an equation exists in arbitrary interval (0,b], provided nonlinear term obeys the respective Lipschitz condition. We prove that each pair of stationary functions of the corresponding R-L derivatives leads to a unique solution in the weighted continuous functions space.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, Czestochowa University of Technology, Czestochowa, Poland

    Marek Błasik & Małgorzata Klimek

Authors
  1. Marek Błasik
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  2. Małgorzata Klimek
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Corresponding author

Correspondence to Marek Błasik .

Editor information

Editors and Affiliations

  1. , Dept. of Automatics & Biomedical Eng., AGH University of Science and Technology, Al. Mickiewicza 20, Cracow, 30-059, Poland

    Wojciech Mitkowski

  2. , Systems Research Institute, Polish Academy of Sciences, Ul. Newelska 6, Warsaw, 01-447, Poland

    Janusz Kacprzyk

  3. , Dept. of Automatics & Biomedical Eng., AGH University of Science and Technology, Al. Mickiewicza 30, Cracow, 30-059, Poland

    Jerzy Baranowski

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Błasik, M., Klimek, M. (2013). Exact Solution of Two-Term Nonlinear Fractional Differential Equation with Sequential Riemann-Liouville Derivatives. In: Mitkowski, W., Kacprzyk, J., Baranowski, J. (eds) Advances in the Theory and Applications of Non-integer Order Systems. Lecture Notes in Electrical Engineering, vol 257. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00933-9_14

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  • DOI: https://doi.org/10.1007/978-3-319-00933-9_14

  • Publisher Name: Springer, Heidelberg

  • Print ISBN: 978-3-319-00932-2

  • Online ISBN: 978-3-319-00933-9

  • eBook Packages: EngineeringEngineering (R0)

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