Abstract: A formulation and solution of the discrete-time fractional optimal control problem in terms of the Caputo fractional derivative is presented in this paper. The performance index (PI) is considered in a quadratic form. The necessary and transversality conditions are obtained using a Hamiltonian approach. Both the free and fixed final state cases have been considered. Numerical examples...

The paper is devoted to the study of an approximation process of time optimal control for fractional evolution systems in Banach spaces. We firstly convert time optimal control problem into Meyer problem. By virtue of the properties of the family of solution operators given by us, the existence of optimal controls for Meyer problem is proved. Secondly, we construct a sequence of Meyer problems ...

In this article we study optimization problems ruled by α-fractional diffusion operators with volume constrains. By means of penalization techniques we prove existence of solutions. We also show that every solution is locally of class C0,α (optimal regularity), and that the free boundary is a C1,α surface, up to a Hn−1-negligible set.