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Path Integral Formulation of Fractional Systems with Multi-Parameters Fractional Derivatives |
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PP: 15-22 |
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doi:10.18576/amisl/130201
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Author(s) |
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S. Muslih,
O. Agrawal,
D. Baleanu,
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Abstract |
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| In this paper, which is based on the recent generalization of fractional variational formulations in terms of multi-parameter fractional derivatives introduced by Agrawal and Muslih, we develop a corresponding path-integral framework for mechanical systems incorporating such operators. We first construct the Lagrangian and Hamiltonian formalisms in the multi-parameter fractional setting, and then derive the associated evolution kernel in the path-integral representation. The resulting formulation offers a unified quantization scheme for systems that exhibit memory and non-local behavior induced by fractional dynamics. Representative examples illustrate the novel features introduced by the multi-parameter derivative structure. |
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