Motion equations and non-Noether symmetries of Lagrangian systems with conformable fractional derivative

In this paper, we present the fractional motion equations and fractional non-Noether symmetries of Lagrangian systems with the conformable fractional derivatives. The exchanging relationship between isochronous variation and fractional derivative, and the fractional Hamilton’s principle of the holonomic conservative and non-conservative systems under the conformable fractional derivative are proposed. Then the fractional motion equations of these systems based on the Hamil¬ton’s principle are established. The fractional Euler operator, the definition of fractional non-Noether symmetries, non-Noether theorem, and Hojman’s conserved quantities for the Lagrangian systems are obtained with conformable fractional derivative. An example is given to illustrate the results.