Invariant conditions for conformable fractional problems of the calculus of variations under the presence of external forces in the dynamics are studied. Depending on the type of transformations considered, different necessary conditions of invariance are obtained. As particular cases, we prove fractional versions of Noether's symmetry theorem. Invariant conditions for fractional optimal control problems, using the Hamiltonian formalism, are also investigated. As an example of potential application in Physics, we show that with conformable derivatives it is possible to formulate an Action Principle for particles under frictional forces that is far simpler than the one obtained with classical fractional derivatives.

This is a preprint of a paper whose final and definite form will appear in the IEEE/CAA Journal of Automatica Sinica, ISSN 2329-9266. Submitted 01-Oct-2015; Revised 20-April-2016; Accepted 22-June-2016