基于联合Caputo导数的分数阶Hamilton力学和分数阶正则变换（英文）

Fractional Hamiltonian mechanics and fractional canonical transformations in terms of a combined Caputo derivative

由于分数阶微积分在科学和工程的诸多领域的成功应用,传统的分析力学理论和方法正在不断地拓展到含有分数阶微积分的系统。基于联合Cuputo分数阶导数,文中建立了分数阶Hamilton原理,并由分数阶Hamilton原理直接导出了分数阶Hamilton正则方程;建立了分数阶力学系统的正则变换理论,给出了四种基本形式的分数阶正则变换,并通过算例说明母函数在分数阶正则变换中的作用。

Traditional theories and methods of analytical mechanics have been expanded to the systems containing frac-tional calculus as the fractional calculus has been successfully used in various scientific fields of engineering. In this pa-per a fractional Hamilton principle for dynamical system defined in terms of combined fractional Cuputo derivatives is es-tablished, from which the fractional Hamilton canonical equations are deduced. Besides, the author presents the theory of fractional canonical transformation within combined fractional Cuputo derivatives and four basic forms of fractional canon-ical transformations. Some examples are given to illustrate the application of the results and the role played by a generat-ing function in the canonical transformation.