Fractional Poisson Bracket

Authors: ALIREZA KHALILI GOLMANKHANEH

Abstract: In the present paper fractional Hamilton-Jacobi equation has been derived for dynamical systems involving the Caputo derivative. Fractional Poisson-bracket is introduced. Further Hamilton's canonical equations are formulated and quantum wave equation corresponds to the fractional Hamilton-Jacobi equation is suggested. Illustrative examples have been worked out to explain the formalism.

Keywords: Hamilton-Jacobi quantized equation; Riemann-Liouville derivative; Caputo derivative; Canonical transformation; Generating function; fractional Poisson-bracket

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