The fractional-order model provides a powerful mathematical tool for the modeling of complex physics,mechanics and engineering problems because of its system openness,time dependence and spatial local-ization.As one of the important contents of analytical mechanics,transformation plays an irreplaceable role in the process of equation simplification and solution.Through canonical transformations,the equations difficult to be solved can be simplified and the form of the original equations remains after transformations.Therefore,it is of great significance to study the canonical transformation of fractional order dynamical systems.This paper studies the canonical transformations of fractional dynamical systems with non-standard Lagrangians,including exponen-tial,power-law and logarithmic Lagrangians.Firstly,fractional generalized momentums and non-standard Hamil-tonians were defined,and Hamilton canonical equations of three kinds of non-standard fractional dynamical sys-tems were derived.Secondly,the criterial equations of canonical transformations of non-standard fractional dy-namical systems were established,and four basic forms of canonical transformations were given according to dif-ferent choices of generating functions.Finally,some examples were given to illustrate the application of the re-sults.
维普
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