Utilizing Fractional Artificial Neural Networks for Modeling Cancer Cell Behavior

In this paper, a novel approach involving a fractional recurrent neural network (RNN) is proposed to achieve the observer-based synchronization of a cancer cell model. According to the properties of recurrent neural networks, our proposed framework serves as a predictive method for the behavior of fractional-order chaotic cancer systems with uncertain orders. Through a stability analysis of weight updating laws, we design a fractional-order Nonlinear Autoregressive with Exogenous Inputs (NARX) network, in which its learning algorithm demonstrates admissible and faster convergence. The main contribution of this paper lies in the development of a fractional neural observer for the fractional-order cancer systems, which is robust in the presence of uncertain orders. The proposed fractional-order model for cancer can capture complex and nonlinear behaviors more accurately than traditional integer-order models. This improved accuracy can provide a more realistic representation of cancer dynamics. Simulation results are presented to demonstrate the effectiveness of the proposed method, where mean square errors of synchronization by applying integer and fractional weight matrix laws are calculated. The density of tumor cell, density of healthy host cell and density of effector immune cell errors for the observer-based synchronization of fractional-order (OSFO) cancer system are less than 0.0.0048, 0.0062 and 0.0068, respectively. Comparative tables are provided to validate the improved accuracy achieved by the proposed framework.