Analogues to Lie Method and Noether's Theorem in Fractal Calculus

GOLMANKHANEH A. K., TUNÇ C.

FRACTAL AND FRACTIONAL, cilt.3, sa.2, 2019 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 3 Sayı: 2
  • Basım Tarihi: 2019
  • Doi Numarası: 10.3390/fractalfract3020025
  • Dergi Adı: FRACTAL AND FRACTIONAL
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

In this manuscript, we study symmetries of fractal differential equations. We show that using symmetry properties, one of the solutions can map to another solution. We obtain canonical coordinate systems for differential equations on fractal sets, which makes them simpler to solve. An analogue for Noether's Theorem on fractal sets is given, and a corresponding conservative quantity is suggested. Several examples are solved to illustrate the results.