We prove optimality conditions for different variational functionals
containing left and right Caputo fractional derivatives. A sufficient condition
of minimization under an appropriate convexity assumption is given. An
Euler-Lagrange equation for functionals where the lower and upper bounds of the
integral are distinct of the bounds of the Caputo derivative is also proved.
Then, the fractional isoperimetric problem is formulated with an integral
constraint also containing Caputo derivatives. Normal and abnormal extremals
are considered.Comment: Submitted 6/March/2010 to Communications in Nonlinear Science and
Numerical Simulation; revised 12/July/2010; accepted for publication
16/July/201
