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Poisson Bracket Formulation for a Dissipative Two- Dimensional Anisotropic Harmonic Oscillator with Fractional Derivatives: Analysis and Applications |
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PP: 59-68 |
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doi:10.18576/pfda/09S106
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Author(s) |
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Bashar M. Al-khamiseh,
Yazen M. Alawaideh,
Samer Alawaideh,
Yasser Aboel-Magd,
Wael Mobarak,
Jihad Asad,
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Abstract |
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| We recast the Harmonic Oscillator using fractional differential equations. to be more developed By applying the Hamiltonian formulation with fractional derivatives to the resulting Harmonic Oscillator. the canonical conjugate- momentum coordinates are defined and converted into operators that fulfill the commutation relations, which correspond to the classical theorys Poisson-bracket relations. The equations of motion are redefined in terms of the generalized brackets when these are generalized. We present a generalized dissipative two-dimensional anisotropic harmonic oscillator equation of motion with fractional derivatives. The novel method was evaluated on a single example and found to be consistent agreement with the classical fractional method.
Keywords: |
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