Abstract
The classical Nambu mechanics is generalized to involve fractional derivatives using two different methods. The first method is based on the definition of fractional exterior derivative and the second one is based on extending the standard velocities to the fractional ones. Fractional Nambu mechanics may be used for nonintegrable systems with memory. Further, Lagrangian which is generate fractional Nambu equations is defined.
Highlights
Derivatives and integrals of fractional-order have found many applications in recent studies in mechanics and physics, for example, in chaotic dynamics, quantum mechanics, plasma physics, anomalous diffusion, and so many fields of physics 1–12
We present the fractional Nambu mechanic based on fractional generalization of the form 3.6
In this part we present the fractional Nambu mechanics based on two Lagrangian formulation
Summary
Derivatives and integrals of fractional-order have found many applications in recent studies in mechanics and physics, for example, in chaotic dynamics, quantum mechanics, plasma physics, anomalous diffusion, and so many fields of physics 1–12 Fractional mechanics describes both conservative and nonconservative systems 13, 14. Riewe has shown that Lagrangian involving fractional time derivatives leads to equation of motion with nonconservative classical derivatives such as friction 13, 14. Motivated by this approach many researchers have explored this area giving new insight into this problem 15–37. In 1973, Nambu generalized Hamiltonian mechanics which is called Nambu mechanics This formalism is shown that provide a suitable framework for the odd Advances in Difference Equations dimensional phase space and nonintegrable systems 39–43.
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