  We study operators that are generalizations of the classical
Riemann-Liouville fractional integral, and of the Riemann-Liouville and Caputo
fractional derivatives. A useful formula relating the generalized fractional
derivatives is proved, as well as three relations of fractional integration by
parts that change the parameter set of the given operator into its dual. Such
results are explored in the context of dynamic optimization, by considering
problems of the calculus of variations with general fractional operators.
Necessary optimality conditions of Euler-Lagrange type and natural boundary
conditions for unconstrained and constrained problems are investigated.
Interesting results are obtained even in the particular case when the
generalized operators are reduced to be the standard fractional derivatives in
the sense of Riemann-Liouville or Caputo. As an application we provide a class
of variational problems with an arbitrary kernel that give answer to the
important coherence embedding problem. Illustrative optimization problems are
considered.
