Implications of non-analytical f(R) gravity at Solar-System scales
  We motivate and analyze the weak-field limit of a non-analytical Lagrangian for the gravitational field. After investigating the parameter space of the model, we impose constraints on the parameters characterizing this class of theories imposed by Solar-System data, i.e. we establish the validity range where this solution applies and refine the constraints by the comparison with planetary orbits. As a result, we claim that this class of models is viable within different astrophysical scales. 
O.M. Lecian, G. Montani