IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v350y2019icp386-401.html
   My bibliography  Save this article

Sumudu transform in fractal calculus

Author

Listed:
  • Golmankhaneh, Alireza K.
  • Tunç, Cemil

Abstract

The Cη-Calculus includes functions on fractal sets, which are not differentiable or integrable using ordinary calculus. Sumudu transforms have an important role in control engineering problems because of preserving units, the scaling property of domains, easy visualization, and transforming linear differential equations to algebraic equations that can be easily solved. Analogues of the Laplace and Sumudu transforms in Cη-Calculus are defined and the corresponding theorems are proved. The generalized Laplace and Sumudu transforms involve functions with totally disconnected fractal sets in the real line. Linear differential equations on Cantor-like sets are solved utilizing fractal Sumudu transforms. The results are summarized in tables and figures. Illustrative examples are solved to give more details.

Suggested Citation

  • Golmankhaneh, Alireza K. & Tunç, Cemil, 2019. "Sumudu transform in fractal calculus," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 386-401.
    • Handle: RePEc:eee:apmaco:v:350:y:2019:i:c:p:386-401
    DOI: 10.1016/j.amc.2019.01.025
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319300347
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.01.025?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. Golmankhaneh, Alireza K. & Tunc, Cemil, 2017. "On the Lipschitz condition in the fractal calculus," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 140-147.
    2. Chen, Wen & Liang, Yingjie, 2017. "New methodologies in fractional and fractal derivatives modeling," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 72-77.
    3. Windus, Alastair Lee & Jensen, Henrik Jeldtoft, 2009. "Change in order of phase transitions on fractal lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(15), pages 3107-3112.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Wu, Junru, 2020. "On a linearity between fractal dimension and order of fractional calculus in Hölder space," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    2. Zhang, Zhiguo & Kon, Mark A., 2022. "Wavelet matrix operations and quantum transforms," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    3. Khalili Golmankhaneh, Alireza & Ontiveros, Lilián Aurora Ochoa, 2023. "Fractal calculus approach to diffusion on fractal combs," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    4. Khalili Golmankhaneh, Alireza & Bongiorno, Donatella, 2024. "Exact solutions of some fractal differential equations," Applied Mathematics and Computation, Elsevier, vol. 472(C).

    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. Serkan Araci & Gauhar Rahman & Abdul Ghaffar & Azeema & Kottakkaran Sooppy Nisar, 2019. "Fractional Calculus of Extended Mittag-Leffler Function and Its Applications to Statistical Distribution," Mathematics, MDPI, vol. 7(3), pages 1-14, March.
    2. Balankin, Alexander S. & Mena, Baltasar, 2023. "Vector differential operators in a fractional dimensional space, on fractals, and in fractal continua," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    3. Khan, Hasib & Ahmad, Farooq & Tunç, Osman & Idrees, Muhammad, 2022. "On fractal-fractional Covid-19 mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    4. Doménech, Antonio, 2009. "A topological phase transition between small-worlds and fractal scaling in urban railway transportation networks?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4658-4668.
    5. Balankin, Alexander S., 2020. "Fractional space approach to studies of physical phenomena on fractals and in confined low-dimensional systems," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    6. Qiu, Lin & Lin, Ji & Chen, Wen & Wang, Fajie & Hua, Qingsong, 2020. "A novel method for image edge extraction based on the Hausdorff derivative," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    7. Nigmatullin, Raoul & Sarkar, Samyadip & Biswas, Karabi, 2021. "New class of fractal elements with log-periodic corrections: Confirmation on experimental data," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).

    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:apmaco:v:350:y:2019:i:c:p:386-401. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.