IntroductionThere are many reasons for developing a mathematical model for an actual plant, among which we may refer to the necessity of designing an identifier in all model-based controller schemes [1]. In dynamic systems, integer order differentiation and partial order differentiation can be used to describe the behaviour of the system. In fractional order differential equations, there is an additional parameter, namely, fractional order, which is important to be selected properly to get better results while modelling and simulating the plant. The fractional order derivative operator is part of the fractional calculus that was introduced 300 years ago. The main advantage of the fractional derivative, in comparison with integer order methods, is that it provides an excellent tool for describing memory and hereditary properties of the processes. This advantage cannot be ignored and as a result, fractional modelling has been employed in different processes [2][3][4][5].Analytical modelling is basically development of a mathematical relationship between input and output based on the physical laws or based on some numerical phenomena. Neural network techniques seem to be very useful to identify different classes of nonlinear systems. Major properties that motivate the use of neural networks are as follows: their nonlinear characteristics make them appropriate for identifying nonlinear systems and their learning characteristics are ideal for adapting to different environmental conditions [6]. Neural networks can be categorized as static (Feedforward) and dynamic (recurrent or differential) neural networks. The main disadvantages of the static structure are as follows: a) slow learning rate, b) lack of possessing memory, so their outputs are uniquely dependent on the current inputs. In contrast, dynamic neural networks can successfully overcome these shortcomings and demonstrate promising behaviour in the presence of un-modelled dynamics because their structure includes an intrinsic feedback. So far, different structures for the integer order dynamic neural network have been used for different applications [7][8][9][10][11].The use of fractional-order models in system identification was initiated in the late 1990s and the beginning of this century. Several techniques are available for identification of the systems