Abstract
In a previous paper [11] we introduced the notion of a \(\mu \)-derivative and showed how to formulate differential equations in terms of this derivative. In this paper, we extend this approach to the definition of a weak derivative which provides a framework for solving variational problems with respect to fractal measures. We apply our method to a specific boundary value problem, namely a 1D eigenvalue problem over a fractal measure.
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Acknowledgements
This research was partially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) in the form of Discovery Grants (HK, FM and ERV).
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Kunze, H., La Torre, D., Mendivil, F., Vrscay, E.R. (2021). Differential Equations Using Generalized Derivatives on Fractals. In: Kilgour, D.M., Kunze, H., Makarov, R., Melnik, R., Wang, X. (eds) Recent Developments in Mathematical, Statistical and Computational Sciences. AMMCS 2019. Springer Proceedings in Mathematics & Statistics, vol 343. Springer, Cham. https://doi.org/10.1007/978-3-030-63591-6_8
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