A discrete time method to the first variation of fractional order variational functionals

Abstract

The fact that the first variation of a variational functional must vanish along an extremizer is the base of most effective solution schemes to solve problems of the calculus of variations. We generalize the method to variational problems involving fractional order derivatives. First order splines are used as variations, for which fractional derivatives are known. The Grunwald-Letnikov definition of fractional derivative is used, because of its intrinsic discrete nature that leads to straightforward approximations.

This is a preprint of a paper whose final and definite form will appear in Central European Journal of Physics. Paper submitted 31-Jan-2013; revised 6-May-2013; accepted for publication 7-May-2013

References in corpus (3)

• Reaction Front in an A+B -> C Reaction-Subdiffusion Process
• Subdiffusion-limited reactions
• Truncation effects in superdiffusive front propagation with Lévy flights

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• A Fourth-Order Compact ADI Scheme for Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation