Abstract
In this paper, the nonconservative systems with second order Lagrangian are investigated using fractional derivatives. The fractional Euler Lagrange equations for these systems are obtained. Then, fractional Hamiltonian for these systems is constructed, which is used to find the Hamilton's equations of motion in the same manner as those obtained by using the formulation of Euler Lagrange equations from variational problems, and it is observed that the Hamiltonian formulation is in exact agreement with the Lagrangian formulation. The passage from the Lagrangian containing fractional derivatives to the Hamiltonian is achieved. We have examined one example to illustrate the formalism.
Highlights
The fractional derivatives have played a significant role in physics, mathematics and engineering [1,2,3,4]
Riewe [5, 6] presented a new approach to mechanics that allows one to obtain the equations for nonconservative systems using fractional derivatives
The formalism for investigating the fractional variational problem of Lagrange represents an important part of fractional calculus and it was discussed by Agrawal [10, 11] and this formalism can be extended to Lagrangian systems with higher derivatives
Summary
The fractional derivatives have played a significant role in physics, mathematics and engineering [1,2,3,4]. The formalism for investigating the fractional variational problem of Lagrange represents an important part of fractional calculus and it was discussed by Agrawal [10, 11] and this formalism can be extended to Lagrangian systems with higher derivatives. In the present paper as a continuation of previous works, the generalized mechanics is considered to obtain the Euler Lagrange equations and Hamilton's equations of motion for nonconservative systems with second order Lagrangians depending on fractional derivatives of coordinates. In Agrawal's work [12] the problem is formulated in term of the left and the right Riemann Liouville fractional derivatives, which is defined as [18].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
