Symmetries, similarity invariant solution, conservation laws and exact solutions of the time-fractional Harmonic Oscillator equation

JOURNAL OF GEOMETRY AND PHYSICS

卷:153

Article

Yourdkhany, Maryam¹  Nadjafikhah, Mehdi² 

[1] Islamic Azad Univ, Dept Math, Karaj Branch, Karaj, Iran

[2] Iran Univ Sci & Technol, Sch Math, Tehran 1684613114, Iran

关键词: Fractional differential equation;    Harmonic Oscillator equation;    Lie symmetry;    Exact solution;    Conservation law;    Invariant sub space;   

DOI  :  10.1016/j.geomphys.2020.103661

来源: Elsevier

【 摘 要 】

In this paper, group analysis of the time-fractional Harmonic Oscillator equation with Riemann-Liouville derivative is performed and its reduced fractional ordinary differential equations are determined. With the aid of the concept of nonlinear self-adjoint and the fractional generalization of the Noether operators are obtained conserved vector for this equation. Furthermore, by using Laplace transform and invariant subspace method, exact solutions of the Riemann-Liouville and Caputo fractional partial differential equations are also constructed. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free