On a new measure on fractals

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Khalili Golmankhaneh A., Baleanu D.

Journal of Inequalities and Applications, cilt.2013, 2013 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2013
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1186/1029-242x-2013-522
  • Dergi Adı: Journal of Inequalities and Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Fractal calculus, Fractal curve, Fractal measure
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

Fractals are sets whose Hausdorff dimension strictly exceeds their topological dimension. The algorithmic Riemannian-like method, Fα-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 Fα-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 Fα-spaces are defined. We suggest the self-adjoint Fα-differential operator so that it can be applied in the fractal quantum mechanics and on the fractal curves. ©2013 Golmankhaneh and Baleanu; licensee Springer.