IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v177y2023ics0960077923011748.html
   My bibliography  Save this article

Neural network operators of generalized fractional integrals equipped with a vector-valued function

Author

Listed:
  • Kadak, Ugur
  • Costarelli, Danilo
  • Coroianu, Lucian

Abstract

In this paper, motivated by the recent development of the approximation capability of neural network operators, we aim to construct neural network (NN) operators for multivariate fractional integrals of order α, which are equipped with a vector-valued function ψ and its Jacobian matrix. In this system, the connection strengths between output neurons are represented by fractional mean values, which depend on the vector-valued function ψ, of the approximated multivariate function. To estimate the rate of convergence (learning rate), the connection weights of NN are equipped with a decreasing sequence (λn). The activation function of the system is constructed using a linear collection ΩΨ, which consists of density functions generated by multivariate sigmoidal functions. Our goal is to construct a flexible and productive hybrid system by leveraging a diverse selection of the function ψ, the parameter α, the sequence (λn) and the activation function ΩΨ. The quantitative estimates of the operators are examined by means of the multivariate modulus of continuity. Moreover, we provide some illustrative examples with graphs to demonstrate the approximation performance of the operators through the selected activation functions. Finally, we present numerical results consisting of the maximum absolute errors of approximation for the proposed operators based on various selections of the vector-valued function ψ.

Suggested Citation

  • Kadak, Ugur & Costarelli, Danilo & Coroianu, Lucian, 2023. "Neural network operators of generalized fractional integrals equipped with a vector-valued function," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:chsofr:v:177:y:2023:i:c:s0960077923011748
    DOI: 10.1016/j.chaos.2023.114272
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923011748
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.114272?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Qian, Yunyou & Yu, Dansheng, 2022. "Rates of approximation by neural network interpolation operators," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    2. Kadak, Ugur, 2022. "Max-product type multivariate sampling operators and applications to image processing," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Costarelli, Danilo & Seracini, Marco & Vinti, Gianluca, 2020. "A comparison between the sampling Kantorovich algorithm for digital image processing with some interpolation and quasi-interpolation methods," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    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. Danilo Costarelli & Michele Piconi & Gianluca Vinti, 2023. "On the convergence properties of sampling Durrmeyer‐type operators in Orlicz spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 296(2), pages 588-609, February.
    2. Cagini, C. & Costarelli, D. & Gujar, R. & Lupidi, M. & Lutty, G.A. & Seracini, M. & Vinti, G., 2022. "Improvement of retinal OCT angiograms by Sampling Kantorovich algorithm in the assessment of retinal and choroidal perfusion," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    3. Arianna Travaglini & Gianluca Vinti & Giovanni Battista Scalera & Michele Scialpi, 2023. "A Large Scale Analysis for Testing a Mathematical Model for the Study of Vascular Pathologies," Mathematics, MDPI, vol. 11(8), pages 1-19, April.
    4. Kadak, Ugur, 2022. "Max-product type multivariate sampling operators and applications to image processing," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

    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:eee:chsofr:v:177:y:2023:i:c:s0960077923011748. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.