New derivatives on the fractal subset of real-line

Khalili Golmankhaneh A., Baleanu D.

Entropy, vol.18, no.2, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 2
  • Publication Date: 2016
  • Doi Number: 10.3390/e18020001
  • Journal Name: Entropy
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Fractal calculus, Generalized beta function, Generalized gamma function, Generalized Mittag-Leffler function, Memory processes, Non-local Laplace transformation, Triadic Cantor set
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this manuscript we introduced the generalized fractional Riemann-Liouville and Caputo like derivative for functions defined on fractal sets. The Gamma, Mittag-Leffler and Beta functions were defined on the fractal sets. The non-local Laplace transformation is given and applied for solving linear and non-linear fractal equations. The advantage of using these new nonlocal derivatives on the fractals subset of real-line lies in the fact that they are better at modeling processes with memory effect.