Fractal calculus involving gauge function

Khalili Golmankhaneh A., Baleanu D.

Communications in Nonlinear Science and Numerical Simulation, cilt.37, ss.125-130, 2016 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 37
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1016/j.cnsns.2016.01.007
  • Dergi Adı: Communications in Nonlinear Science and Numerical Simulation
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.125-130
  • Anahtar Kelimeler: Fractal calculus, Fractal dimension, Fractional derivative, Gauge integral
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

Henstock-Kurzweil integral or gauge integral is the generalization of the Riemann integral. The functions which are not integrable because of singularity in the senses of Lebesgue or Riemann are gauge integrable.In this manuscript, we have generalized Fα-calculus using the gauge integral method for the integrating of the functions on fractal set subset of real-line where they have singularities. The suggested new method leads to the wider class of functions on the fractal subset of real-line that are *Fα-integrable. Using gauge function we define *Fα-derivative of functions their Fα-derivative is not exist. The reported results can be used for generalizing the fundamental theorem of Fα-calculus.