This paper deals with two synthesis methods of a limited-bandwidth fractional integrator by using the link with the localised parameter systems, called networks. The first, from the concept to the achievement, presents the different steps to determine the parametric values of the RC cells that compose the networks used for the synthesis. The second, from the achievement to the concept, presents the optimal conditions necessary to obtain a limited-bandwidth fractional integrator from a particular network of N+1 identical RC cells, in particular with N small. To illustrate, an example is given with N = 4 and a fractional order of 0.578, the value being determined first with an analytical approach, then with an experimental approach.