Transactions of Nanjing University of Aeronautics & Astronautics
Generalized Canonical Transformations for Fractional Birkhoffian Systems
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Abstract:
This paper presents fractional generalized canonical transformations for fractional Birkhoffian systems within Caputo derivatives. Firstly， based on fractional Pfaff-Birkhoff principle within Caputo derivatives， fractional Birkhoff’s equations are derived and the basic identity of constructing generalized canonical transformations is proposed. Secondly， according to the fact that the generating functions contain new and old variables， four kinds of generating functions of the fractional Birkhoffian system are proposed， and four basic forms of fractional generalized canonical transformations are deduced. Then， fractional canonical transformations for fractional Hamiltonian system are given. Some interesting examples are finally listed.
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This work was supported by the National Natural Science Foundations of China （Nos.11972241， 11572212， 11272227） and the Natural Science Foundation of Jiangsu Province （No. BK20191454）.
Clc Number:
O316
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