Construction of some new fractional canonical transformations  and their generating functions

F  A  Abd El Salam

doi:10.17485/ijst/2012/v5i10.3

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$Construction of some new fractional canonical transformations and their generating functions$

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2012/v5i10.3

Year: 2012, Volume: 5, Issue: 10, Pages: 1-8

Original Article

Construction of some new fractional canonical transformations and their generating functions

F. A. Abd El-Salam

¹ Current Address: Taibah University, Faculty of Science, Department of Mathematics, 2 Permanent Address: Cairo University, Faculty of Science, Department of Astronomy, Cairo, 12613, Egypt f.a.abde[email protected]

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

The Fractional Calculus, in brief FC generalizes the differentiation and integration from integer to rational order. It enables us to derive equations of motion with non conservative classical forces using fractional Lagrangians. In this paper fundamental properties of fractional derivative are outlined. The behavior of some elementary functions under the effect of the fractional differintegral operator is examined. Using the Riemann-Liouville differintegral, Fractional Euler-Lagrange equation is obtained. Fractional Hamilton’s canonical equations are formulated. Different canonical transformations with different generating functions are derived. Fractional Poisson bracket is introduced. Fractional Hamilton-Jacobi equation is presented.
Keywords: Riemann-Liouville derivative; Fractional Euler-Lagrange equation; Fractional Hamilton’s canonical equations.