IDEAS home Printed from https://ideas.repec.org/a/hin/jjopti/142390.html
   My bibliography  Save this article

Optimization of Integer Order Integrators for Deriving Improved Models of Their Fractional Counterparts

Author

Listed:
  • Maneesha Gupta
  • Richa Yadav

Abstract

Second and third order digital integrators (DIs) have been optimized first using Particle Swarm Optimization (PSO) with minimized error fitness function obtained by registering mean, median, and standard deviation values in different random iterations. Later indirect discretization using Continued Fraction Expansion (CFE) has been used to ascertain a better fitting of proposed integer order optimized DIs into their corresponding fractional counterparts by utilizing their refined properties, now restored in them due to PSO algorithm. Simulation results for the comparisons of the frequency responses of proposed 2nd and 3rd order optimized DIs and proposed discretized mathematical models of half integrators based on them, with their respective existing operators, have been presented. Proposed integer order PSO optimized integrators as well as fractional order integrators (FOIs) have been observed to outperform the existing recently published operators in their respective domains reasonably well in complete range of Nyquist frequency.

Suggested Citation

  • Maneesha Gupta & Richa Yadav, 2013. "Optimization of Integer Order Integrators for Deriving Improved Models of Their Fractional Counterparts," Journal of Optimization, Hindawi, vol. 2013, pages 1-11, June.
    • Handle: RePEc:hin:jjopti:142390
    DOI: 10.1155/2013/142390
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/7179/2013/142390.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/7179/2013/142390.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/142390?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Lokenath Debnath, 2003. "Recent applications of fractional calculus to science and engineering," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-30, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Musrrat Ali & Hemant Gandhi & Amit Tomar & Dimple Singh, 2023. "Similarity Solution for a System of Fractional-Order Coupled Nonlinear Hirota Equations with Conservation Laws," Mathematics, MDPI, vol. 11(11), pages 1-14, May.
    2. Xing, Sheng Yan & Lu, Jun Guo, 2009. "Robust stability and stabilization of fractional-order linear systems with nonlinear uncertain parameters: An LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1163-1169.
    3. Liaqat, Muhammad Imran & Akgül, Ali, 2022. "A novel approach for solving linear and nonlinear time-fractional Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    4. Boukhouima, Adnane & Hattaf, Khalid & Lotfi, El Mehdi & Mahrouf, Marouane & Torres, Delfim F.M. & Yousfi, Noura, 2020. "Lyapunov functions for fractional-order systems in biology: Methods and applications," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Laarem, Guessas, 2021. "A new 4-D hyper chaotic system generated from the 3-D Rösslor chaotic system, dynamical analysis, chaos stabilization via an optimized linear feedback control, it’s fractional order model and chaos sy," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    6. Ravi Kanth, A.S.V. & Devi, Sangeeta, 2021. "A practical numerical approach to solve a fractional Lotka–Volterra population model with non-singular and singular kernels," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    7. Jehad Alzabut & Weerawat Sudsutad & Zeynep Kayar & Hamid Baghani, 2019. "A New Gronwall–Bellman Inequality in Frame of Generalized Proportional Fractional Derivative," Mathematics, MDPI, vol. 7(8), pages 1-15, August.
    8. Iyiola, O.S. & Tasbozan, O. & Kurt, A. & Çenesiz, Y., 2017. "On the analytical solutions of the system of conformable time-fractional Robertson equations with 1-D diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 94(C), pages 1-7.
    9. Anague Tabejieu, L.M. & Nana Nbendjo, B.R. & Filatrella, G., 2019. "Effect of the fractional foundation on the response of beam structure submitted to moving and wind loads," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 178-188.
    10. Ning, Xin & Ma, Yanyan & Li, Shuai & Zhang, Jingmin & Li, Yifei, 2018. "Response of non-linear oscillator driven by fractional derivative term under Gaussian white noise," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 102-107.
    11. Anague Tabejieu, L.M. & Nana Nbendjo, B.R. & Woafo, P., 2016. "On the dynamics of Rayleigh beams resting on fractional-order viscoelastic Pasternak foundations subjected to moving loads," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 39-47.
    12. Mian Bahadur Zada & Muhammad Sarwar & Thabet Abdeljawad & Aiman Mukheimer, 2021. "Coupled Fixed Point Results in Banach Spaces with Applications," Mathematics, MDPI, vol. 9(18), pages 1-12, September.
    13. Lashkarian, Elham & Reza Hejazi, S., 2017. "Group analysis of the time fractional generalized diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 572-579.
    14. Kumar, Devendra & Nama, Hunney & Baleanu, Dumitru, 2024. "Dynamical and computational analysis of fractional order mathematical model for oscillatory chemical reaction in closed vessels," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    15. Majumdar, Prahlad & Mondal, Bapin & Debnath, Surajit & Ghosh, Uttam, 2022. "Controlling of periodicity and chaos in a three dimensional prey predator model introducing the memory effect," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    16. Tabatabaei-Nejhad, Seyede Zahra & Eghtesad, Mohammad & Farid, Mehrdad & Bazargan-Lari, Yousef, 2022. "Combination of fractional-order, adaptive second order and non-singular terminal sliding mode controls for dynamical systems with uncertainty and under-actuation property," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    17. Erman, Sertaç & Demir, Ali, 2020. "On the construction and stability analysis of the solution of linear fractional differential equation," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    18. Serik Aitzhanov & Kymbat Bekenayeva & Zamira Abdikalikova, 2023. "Boundary Value Problem for a Loaded Pseudoparabolic Equation with a Fractional Caputo Operator," Mathematics, MDPI, vol. 11(18), pages 1-12, September.
    19. Songshu Liu, 2022. "Recovering a Space-Dependent Source Term in the Fractional Diffusion Equation with the Riemann–Liouville Derivative," Mathematics, MDPI, vol. 10(17), pages 1-13, September.
    20. Sivaporn Ampun & Panumart Sawangtong, 2021. "The Approximate Analytic Solution of the Time-Fractional Black-Scholes Equation with a European Option Based on the Katugampola Fractional Derivative," Mathematics, MDPI, vol. 9(3), pages 1-15, January.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:jjopti:142390. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.