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A Fractional Order Dynamical Trajectory Approach for Optimization Problem with HPM

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Fractional Dynamics and Control

Abstract

In this paper, the homotopy perturbation method (HPM) is applied to solve nonlinear programming (NLP) problem on the basis of the fractional order differential equations system. The trajectory of the proposed fractional order dynamical system is approached to the optimal solution for optimization problem. The multistage strategy is used to show this behavior of the system trajectory in large timespan. The ability of the method to obtain approximate analytical solutions was shown by comparisons among the multistage HPM, the standard HPM and the fourth order Runge–Kutta method.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Balıkesir University, Çag̃ış Campus, 10145, Balıkesir, Turkey

    Firat Evirgen & Necati Özdemir

Authors
  1. Firat Evirgen
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  2. Necati Özdemir
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Corresponding author

Correspondence to Firat Evirgen .

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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Evirgen, F., Özdemir, N. (2012). A Fractional Order Dynamical Trajectory Approach for Optimization Problem with HPM. 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_12

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  • DOI: https://doi.org/10.1007/978-1-4614-0457-6_12

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-0456-9

  • Online ISBN: 978-1-4614-0457-6

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