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Sumudu transform in fractal calculus

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. Golmankhaneh, Alireza K. & Tunc, Cemil, 2017. "On the Lipschitz condition in the fractal calculus," Chaos, Solitons & Fractals, Elsevier, vol. 95(C), pages 140-147.
    3. Chen, Wen & Liang, Yingjie, 2017. "New methodologies in fractional and fractal derivatives modeling," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 72-77.
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    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).

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