Solving fractal differential equations via fractal Laplace transforms

Kamal Ali K., Khalili Golmankhaneh A., Yilmazer R., Ashqi Abdullah M.

Journal of Applied Analysis, cilt.28, sa.2, ss.237-250, 2022 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 28 Sayı: 2
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1515/jaa-2021-2076
  • Dergi Adı: Journal of Applied Analysis
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, ABI/INFORM, zbMATH
  • Sayfa Sayıları: ss.237-250
  • Anahtar Kelimeler: Fractal calculus, fractal convolution theorem, fractal Laplace transform, fractal Wright function
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

The intention of this study is to investigate the fractal version of both one-term and three-term fractal differential equations. The fractal Laplace transform of the local derivative and the non-local fractal Caputo derivative is applied to investigate the given models. The analogues of both the Wright function with its related definitions in fractal calculus and the convolution theorem in fractal calculus are proposed. All results in this paper have been obtained by applying certain tools such as the general Wright and Mittag-Leffler functions of three parameters and the convolution theorem in the sense of the fractal calculus. Moreover, a comparative analysis is conducted by solving the governing equation in the senses of the standard version and fractal calculus. It is obvious that when α = γ = β = 1 {\alpha=\gamma=\beta=1}, we obtain the same results as in the standard version.