Variational problems with Hadamard type fractional integrals

This paper is devoted to the study of variational problems with Hadamard type fractional integrals. We present two approaches to solve such type of variational problems: indirect and direct. In the first case we derive necessary optimality conditions which reduce the problem to one involving a fractional integral equation. In the second case a discretization method which transforms the variational problem into a static multi-variable optimization problem is presented.