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.