English

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.

Keywords

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)

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