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

GOLMANKHANEH A., TUNÇ C.

FRACTAL AND FRACTIONAL, vol.3, no.2, 2019 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 3 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.3390/fractalfract3020025
  • Journal Name: FRACTAL AND FRACTIONAL
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

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.