Battery discharging model on fractal time sets

Ali K. K., Khalili Golmankhaneh A., Yilmazer R.

International Journal of Nonlinear Sciences and Numerical Simulation, cilt.24, sa.1, ss.71-80, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 24 Sayı: 1
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1515/ijnsns-2020-0139
  • Dergi Adı: International Journal of Nonlinear Sciences and Numerical Simulation
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.71-80
  • Anahtar Kelimeler: fractal calculus, the fractal battery discharging equation, the local fractal Laplace transform, the non-local fractal transform
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

This article is devoted to propose and investigate the fractal battery discharging model, which is one of the well-known models with a memory effect. It is presented as to how non-locality affects the behavior of solutions and how the current state of the system is affected by its past. Firstly, we present a local fractal solution. Then we solve the non-local fractal differential equation and examine the memory effect that includes the Mittag-Leffler function with one parameter. For that aim, the local fractal and non-local fractal Laplace transforms are used to achieve fractional solutions. In addition, the simulation analysis is performed by comparing the underlying fractal derivatives to the classical ones in order to understand the significance of the results. The effects of the fractal parameter and the fractional parameter are discussed in the conclusion section.