Baleanu, DumitruGolmankhaneh, Alireza K.2022-10-062025-09-182022-10-062025-09-182013Golmankhaneh, Alireza K.; Baleanu, Dumitru (2013). "On a new measure on fractals", Journal of Inequalities and Applications, Vol. 2013.1029-242Xhttps://doi.org/10.1186/1029-242X-2013-522https://hdl.handle.net/20.500.12416/11115Khalili Golmankhaneh, Alireza/0000-0002-5008-0163Fractals are sets whose Hausdorff dimension strictly exceeds their topological dimension. The algorithmic Riemannian-like method, F-alpha-calculus, has been suggested very recently. Henstock-Kurzweil integral is the generalized Riemann integral method by using the gauge function. In this paper we generalize the F-alpha-calculus as a fractional local calculus that is more suitable to describe some physical process. We introduce the new measure using the gauge function on fractal sets that gives a finer dimension in comparison with the Hausdorff and box dimension. Hilbert F-alpha-spaces are defined. We suggest the self-adjoint F-alpha-differential operator so that it can be applied in the fractal quantum mechanics and on the fractal curves.eninfo:eu-repo/semantics/openAccessFractal MeasureFractal CalculusFractal CurveArticle10.1186/1029-242X-2013-5222-s2.0-84897584668