SpringerIranian Journal of Science and Technology (Sciences)1028-627637320130812Fractional lie series and transforms as canonical mappings
Dr. Abd El-Salam199210159510.22099/ijsts.2013.1595ENF. A.Abd El-SalamJournal Article20111122Using the Riemann-Liouville fractional differintegral operator, the Lie theory is reformulated. The fractional <br />Poisson bracket over the fractional phase space as 3N state vector is defined to be the fractional Lie derivative. Its <br />properties are outlined and proved. A theorem for the canonicity of the transformation using the exponential <br />operator is proved. The conservation of its generator is proved in a corollary. A Theorem for the inverse fractional <br />canonical mapping is proved. The composite mappings of two successive transformations is defined. The <br />fractional Lie operator and its properties are introduced. Some useful lemmas on this operator are proved. Lie <br />transform depending on a parameter over the fractional phase space is presented and its relations are proved. Two <br />theorems that proved the transformation <br /><span style="font-family: Symbol; font-size: x-small;" lang="ZH-TW"><span style="font-family: Symbol; font-size: x-small;" lang="ZH-TW"> </span></span><span style="font-family: Times New Roman; font-size: x-small;"><span style="font-family: Times New Roman; font-size: x-small;">= </span></span><em><span style="font-family: Times New Roman; font-size: x-small;"><span style="font-family: Times New Roman; font-size: x-small;">E</span></span><span style="font-family: Times New Roman; font-size: xx-small;"><em><span style="font-family: Times New Roman; font-size: xx-small;">W </span></em></span></em><span style="font-family: Times New Roman; font-size: x-small;"><span style="font-family: Times New Roman; font-size: x-small;">Z </span></span><br /><span style="font-family: Times New Roman; font-size: xx-small;">is completely canonical and is a solution of the Hamiltonian</span> <br />system (30) are given. Recurrence relations are obtained. <br /> <br /> http://ijsts.shirazu.ac.ir/article_1595_81bd26c3967e9204c061abdfa89f08a1.pdf