Generalization of Mei symmetry approach to fractional Birkhoffian mechanics

• Published in: Chaos, solitons and fractals Vol. 166; p. 112971
• Main Authors: Zhang, Yi, Jia, Yun-Die
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.01.2023
• Subjects: Fractional Birkhoffian system; Mei conserved quantity; Mei symmetry; Quasi-fractional dynamics model; Mei conserved quantity; Mei symmetry; Quasi-fractional dynamics model; Fractional Birkhoffian system
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2022.112971

The fractional Birkhoffian systems are investigated for Mei symmetry and corresponding conserved quantities. It is divided into two cases, one is standard fractional Birkhoffian systems, the other is fractional Birkhoffian systems under quasi-fractional dynamics models of El-Nabulsi type. The fractional Pfaff-Birkhoff principles are presented, and Birkhoff’s equations are deduced. Mei symmetry and its determining equations are established. Mei symmetry theorems are proved and fractional conserved quantities are obtained. •The fractional Pfaff-Birkhoff principles and Birkhoff’s equations are established.•A new kind of conserved quantities for fractional Birkhoffian systems are obtained.•Mei symmetry theorems for fractional Birkhoffian systems are proposed and proved, and extended to quasi-fractional dynamics models.