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This paper provides necessary and sufficient conditions of optimalityfor variational problems that deal with a fractional derivative with respectto another function. Fractional Euler–Lagrange equations are established forthe fundamental problem and when in presence of an integral constraint. ALegendre condition, which is a second-order necessary condition, is also obtained.Other cases, such as the infinite horizon problem, the problem withdelays in the Lagrangian, and the problem with high-order derivatives, areconsidered. Finally, a necessary condition for the optimal fractional order tosatisfy is proved

Optimality conditions for fractional variational problems with free terminal time