Helmholtz theorem for nondifferentiable Hamiltonian systems in the   framework of Cresson's quantum calculus
  We derive the Helmholtz theorem for nondifferentiable Hamiltonian systems in the framework of Cresson's quantum calculus. Precisely, we give a theorem characterizing nondifferentiable equations, admitting a Hamiltonian formulation. Moreover, in the affirmative case, we give the associated Hamiltonian. 
Fr\'ed\'eric Pierret and Delfim F. M. Torres
math.OC math.FA