Symmetries and conserved quantities for fractional action-like Pfaffian variational problems

Abstract

The fractional Pfaffian variational problems and the fractional Noether theory are studied under a fractional model presented by El-Nabulsi. Firstly, the fractional action-like Pfaffian variational problem is presented, the El-Nabulsi–Pfaff–Birkhoff–d’Alembert fractional principle is established, then the El-Nabulsi–Birkhoff fractional equations are derived; secondly, the definitions and criteria of the fractional Noether symmetric transformations are given, which are based on the invariance of El-Nabulsi–Pfaffian action under the infinitesimal transformations of group, then the inner relationship between a fractional Noether symmetry and a fractional conserved quantity is established; finally, two examples are given to illustrate the application of the results.