A study on fractional cancer model using neural network scheme based on PINN–ASBO

A tumour is a mass or lump of tissue that forms when abnormal cells aggregate, posing a serious and harmful health risk. In this study, we develop a fractional-order cancer immune dynamical model to compare tumour cells and effector cells. Our primary objective is to introduce a neural network-based method for solving the fractional-order cancer model. We apply the average and subtraction-based optimisation (ASBO) method to solve the model. ASBO is a three-step optimisation method which gives us accurate results. We analyse it using Levenberg–Marquardt neural networks (LMNNs). The robustness and versatility of the ASBO algorithm enable it to converge rapidly to the ideal values. We examine the interactions between tumour cells and immune cells, thereby simulating a real-world medical research problem that aids model construction. Using the Jacobian matrix, we establish the model’s stability and prove ULAM’s stability. We solve the problem with a neural network containing 20 neurons. The LMNN approach applies supervised learning, where we use 80% of the data for training, 15% for validation and 5% for testing. We assess the efficacy and accuracy of LMNNs through regression plots, correlation analysis, histogram curves and function tests. We also employ the Adams–Bashforth–Moulton (ABM) predictor–corrector method to compare with our solutions. We generate all graphical results in MATLAB. The findings of this investigation will support biologists in the treatment of cancer.