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A Note on the Sequential Linear Fractional Dynamical Systems from the Control System Viewpoint and L 2 -Theory

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Fractional Dynamics and Control

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Abstract

In this chapter, we consider a sequential linear fractional differential equation with constant coefficients. After deriving a closed analytical solution based on the sequential fractional derivatives, we propose a theorem that gives some weak conditions under which any arbitrary function in L 2 can be approximated by an output of a linear time-invariant fractional differential equation. More precisely, we prove that all L 2 functions can be represented as the L 2 limit of functions that are the outputs of fractional linear control systems. The analysis is developed in the Hilbert space.

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Author information

Authors and Affiliations

  1. Intelligent Control Systems Laboratory, School of Electrical and Computer Engineering, Tarbiat Modares University, Tehran, Iran

    Abolhassan Razminia & Vahid Johari Majd

  2. Department of Engineering Science, School of Engineering, University of Tehran, Tehran, Iran

    Ahmad Feiz Dizaji

Authors
  1. Abolhassan Razminia
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  2. Vahid Johari Majd
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  3. Ahmad Feiz Dizaji
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Corresponding author

Correspondence to Vahid Johari Majd .

Editor information

Editors and Affiliations

  1. Faculty of Art and Sciences, Mathematics and Computer Sciences, Cankaya University, Ankara, Turkey

    Dumitru Baleanu

  2. Institute of Engineering, Department of Electrical Engineering, Polytechnic Institute of Porto, Rua Dr António Bernadino Almeida 431, Porto, 4200-072, Portugal

    José António Tenreiro Machado

  3. Edwardsville, School of Engineering, Southern Illinois University, Room: EB2064, Edwardsville, 62026-1805, USA

    Albert C. J. Luo

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Razminia, A., Majd, V.J., Dizaji, A.F. (2012). A Note on the Sequential Linear Fractional Dynamical Systems from the Control System Viewpoint and L 2 -Theory. In: Baleanu, D., Machado, J., Luo, A. (eds) Fractional Dynamics and Control. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0457-6_6

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  • DOI: https://doi.org/10.1007/978-1-4614-0457-6_6

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-0456-9

  • Online ISBN: 978-1-4614-0457-6

  • eBook Packages: EngineeringEngineering (R0)

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