73 research outputs found
Towards a combined fractional mechanics and quantization
A fractional Hamiltonian formalism is introduced for the recent combined
fractional calculus of variations. The Hamilton-Jacobi partial differential
equation is generalized to be applicable for systems containing combined Caputo
fractional derivatives. The obtained results provide tools to carry out the
quantization of nonconservative problems through combined fractional canonical
equations of Hamilton type.Comment: This is a preprint of a paper whose final and definite form will be
published in: Fract. Calc. Appl. Anal., Vol. 15, No 3 (2012). Submitted
21-Feb-2012; revised 29-May-2012; accepted 03-June-201
The generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative
This paper presents necessary and sufficient optimality conditions for
problems of the fractional calculus of variations with a Lagrangian depending
on the free end-points. The fractional derivatives are defined in the sense of
Caputo.Comment: Accepted (19 February 2010) for publication in Computers and
Mathematics with Application
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