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Symmetries, similarity invariant solution, conservation laws and exact solutions of the time-fractional Harmonic Oscillator equation
تقارن ، راه حل ثابت مشابه ، قوانین حفاظت و راه حل های دقیق معادله نوسانگر هارمونیک کسری زمانی-2020 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. Keywords: Fractional differential equation | Harmonic Oscillator equation | Lie symmetry | Exact solution | Conservation law | Invariant sub space |
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