Baleanu, D.Baleanu, DumitruAsad, J. H.Petras, I.Elagan, S.Bilgen, A.Matematik02.02. Matematik02. Fen-Edebiyat Fakültesi01. Çankaya Üniversitesi2025-09-232025-09-232012Baleanu, D...et al. (2012). "FRACTIONAL EULER-LAGRANGE EQUATION OF CALDIROLA-KANAI OSCILLATOR, Romanian Reports In Physics, Vol. 64, pp. 1171-1177.1221-14511841-8759https://hdl.handle.net/20.500.12416/15582Petras, Ivo/0000-0002-9250-6986; Asad, Jihad/0000-0002-6862-1634; Elagan, Sayed/0000-0003-4781-5445A study of the fractional Lagrangian of the so-called Caldirola-Kanai oscillator is presented. The fractional Euler-Lagrangian equations of the system have been obtained, and the obtained Euler-Lagrangian equations have been studied numerically. The numerical study is based on the so-called Grunwald-Letnikov approach, which is power series expansion of the generating function (backward and forward difference) and it can be easy derived from the Grunwald-Letnikov definition of the fractional derivative. This approach is based on the fact, that Riemman-Liouville fractional derivative is equivalent to the Grunwald-Letnikov derivative for a wide class of the functions.eninfo:eu-repo/semantics/closedAccessRiemann-Liouville DerivativesCaldirola-Kanai OscillatorGrunwald-Letnikov ApproachArticle2-s2.0-84879528675