Higher order fractal differential equations

Khalili Golmankhaneh A., Depollier C., Pham D.

Modern Physics Letters A, cilt.39, sa.27-28, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 39 Sayı: 27-28
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1142/s021773232450127x
  • Dergi Adı: Modern Physics Letters A
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, zbMATH
  • Anahtar Kelimeler: Fractal calculus, higher homogeneous fractal di®erential equations, higher nonhomogeneous, nonhomogeneous
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

This paper provides a summary of the fractal calculus framework. It presents higher-order homogeneous and nonhomogeneous linear fractal di®erential equations with α-order. Solutions for these equations with constant coe±cients are obtained through the method of variation of parameters and the method of undetermined coe±cients. The solution space for higher α-order linear fractal di®erential equations is defined, showcasing its non-integer dimensionality. The solutions to α-order linear fractal di®erential equations are graphically depicted to illustrate their non-di®erentiability. Additionally, equations of motion governing the behavior of two masses in fractal time are proposed and solved.