A Fractional Calculus of Variations for Multiple Integrals with Application to Vibrating String
Optimization and Control
2010-03-09 v1 Mathematical Physics
math.MP
Abstract
We introduce a fractional theory of the calculus of variations for multiple integrals. Our approach uses the recent notions of Riemann-Liouville fractional derivatives and integrals in the sense of Jumarie. Main results provide fractional versions of the theorems of Green and Gauss, fractional Euler-Lagrange equations, and fractional natural boundary conditions. As an application we discuss the fractional equation of motion of a vibrating string.
Cite
@article{arxiv.1001.2722,
title = {A Fractional Calculus of Variations for Multiple Integrals with Application to Vibrating String},
author = {Ricardo Almeida and Agnieszka B. Malinowska and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:1001.2722},
year = {2010}
}
Comments
Accepted for publication in the Journal of Mathematical Physics (14/January/2010)