Fractal Mellin transform and non-local derivatives

Khalili Golmankhaneh A., Welch K., Serpa C., Jørgensen P. E. T.

Georgian Mathematical Journal, cilt.31, sa.3, ss.423-436, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 31 Sayı: 3
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1515/gmj-2023-2094
  • Dergi Adı: Georgian Mathematical Journal
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, zbMATH
  • Sayfa Sayıları: ss.423-436
  • Anahtar Kelimeler: Fractal local Mellin transform, fractal non-local derivatives., fractal non-local transform
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

This paper provides a comparison between the fractal calculus of fractal sets and fractal curves. There are introduced the analogues of the Riemann-Liouville and Caputo integrals and derivatives for fractal curves, which are non-local derivatives. Moreover, the concepts analogous to the fractional Laplace operator to address fractal non-local differential equations on fractal curves are defined. Additionally, in the paper it is introduced the fractal local Mellin transform and fractal non-local transform as tools for solving fractal differential equations. The results are supported with tables and examples to demonstrate the findings.