A formulation for fractional optimal control problems via left and right caputo derivatives

This paper formulates and investigates the Fractional Optimal Control Problems (FOCPs) of systems displaying fractional dynamics in terms of the Left and the Right Caputo derivatives. We obtains the fractional Euler-Lagrange equations and the transversality conditions by utilizing the fractional calculus of variations, the Lagrange multiplier technique and the formulae for fractional integration by parts. Several cases are considered: the final time is fixed or unspecified, while the corresponding final state is fixed, constrained or unspecified. The proposed formulations, along with the resulting Euler-Lagrange equations and the transversality conditions are very similar to those for classical optimal control problems.