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Hyers–Ulam stability on local fractal calculus and radioactive decay

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Abstract

In this paper, we summarize the local fractal calculus, called \(F^{\alpha }\)-calculus, which defines derivatives and integrals of functions with fractal domains of non-integer dimensions, functions for which ordinary calculus fails. Hyers–Ulam stability provides a method to find approximate solutions for equations where the exact solution cannot be found. Here, we generalize Hyers–Ulam stability to be applied to \(\alpha \)-order linear fractal differential equations. The nuclear decay law involving fractal time is suggested, and it is proved to be fractally Hyers–Ulam stable.

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  • 27 November 2021

    The change has to be made due to a typo in the Acknowledgements.

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Acknowledgements

A.K.G dedicates this article to his supervisor during his Ph.D., Professor A. D. Gangal, to whom he owes all he has learned on the subject of fractal calculus and scientific success, and he also wishes him and his respected family good health and the best.

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Authors and Affiliations

  1. Department of Physics, Urmia Branch, Islamic Azad University, Urmia, Iran

    Alireza Khalili Golmankhaneh

  2. Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Campus, 65080, Van, Turkey

    Cemil Tunç

  3. Department of Computer Engineering, Faculty of Engineering, Van Yuzuncu Yil University, Campus, 65080, Van, Turkey

    Hamdullah Şevli

Authors
  1. Alireza Khalili Golmankhaneh
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  2. Cemil Tunç
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  3. Hamdullah Şevli
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Correspondence to Alireza Khalili Golmankhaneh.

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Khalili Golmankhaneh, A., Tunç, C. & Şevli, H. Hyers–Ulam stability on local fractal calculus and radioactive decay. Eur. Phys. J. Spec. Top. 230, 3889–3894 (2021). https://doi.org/10.1140/epjs/s11734-021-00316-5

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  • DOI: https://doi.org/10.1140/epjs/s11734-021-00316-5

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