Existence of solution for a class of fractional Hamiltonian systems

TL;DR

This paper proves the existence of solutions for a class of fractional Hamiltonian systems involving fractional derivatives and variable coefficients, expanding the understanding of such systems in mathematical physics.

Contribution

It establishes new existence results for fractional Hamiltonian systems with variable coefficients using variational methods.

Findings

Existence of solutions proven under certain conditions.

Application of variational methods to fractional systems.

Extension of classical Hamiltonian system results to fractional context.

Abstract

In this work we want to prove the existence of solution for a class of fractional Hamiltonian systems given by {eqnarray*}_{t}D_{\infty}^{\alpha}(_{-\infty}D_{t}^{\alpha}u(t)) + L(t)u(t) = & \nabla W(t,u(t)) u\in H^{\alpha}(\mathbb{R}, \mathbb{R}^{N}) {eqnarray*}