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On a linearity between fractal dimension and order of fractional calculus in Hölder space

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  • Wu, Junru

Abstract

In this paper, the linear relationship between fractal dimensions and the order of fractional calculus of functions in Hölder space has been mainly investigated. Under specific Hölder condition, the linear connection between Box dimension and the order of Riemann-Liouville fractional integral and derivative has been proved. This linear connection is also established with K-dimension and Packing dimension. Some function examples have been given in the end.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:385:y:2020:i:c:s0096300320303945
    DOI: 10.1016/j.amc.2020.125433
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    References listed on IDEAS

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    1. Wen, Chunhui & Yang, Jinhai, 2019. "Complexity evolution of chaotic financial systems based on fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 242-251.
    2. Golmankhaneh, Alireza K. & Tunç, Cemil, 2019. "Sumudu transform in fractal calculus," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 386-401.
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    Cited by:

    1. Wang, Yupin & Li, Xiaodi & Wang, Da & Liu, Shutang, 2022. "A brief note on fractal dynamics of fractional Mandelbrot sets," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    2. Yu, Binyan & Liang, Yongshun, 2024. "On two special classes of fractal surfaces with certain Hausdorff and Box dimensions," Applied Mathematics and Computation, Elsevier, vol. 468(C).
    3. Khalili Golmankhaneh, Alireza & Tejado, Inés & Sevli, Hamdullah & Valdés, Juan E. Nápoles, 2023. "On initial value problems of fractal delay equations," Applied Mathematics and Computation, Elsevier, vol. 449(C).

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