Fractional Hamilton’s Canonical Equations and Poisson Theorem of Mechanical Systems with Fractional Factor

Linli Wang (), Jingli Fu and Liangliang Li
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Linli Wang: School of Mathematics and Statistics, Xinxiang University, Xinxiang 453000, China
Jingli Fu: College of Information and Control Engineering, Shandong Vocational University of Foreign Affairs, Weihai 264504, China
Liangliang Li: Department of Electronic Engineering, Tsinghua University, Beijing 100084, China

Mathematics, 2023, vol. 11, issue 8, 1-13

Abstract: Because of the nonlocal and nonsingular properties of fractional derivatives, they are more suitable for modelling complex processes than integer derivatives. In this paper, we use a fractional factor to investigate the fractional Hamilton’s canonical equations and fractional Poisson theorem of mechanical systems. Firstly, a fractional derivative and fractional integral with a fractional factor are presented, and a multivariable differential calculus with fractional factor is given. Secondly, the Hamilton’s canonical equations with fractional derivative are obtained under this new definition. Furthermore, the fractional Poisson theorem with fractional factor is presented based on the Hamilton’s canonical equations. Finally, two examples are given to show the application of the results.

Keywords: fractional factor; fractional Hamilton’s canonical equations; fractional Poisson theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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