A Bernstein Polynomial-Based Neural Network Framework for Solving Fractional Tumor Growth Mathematical Model

Abstract This paper presents a novel approach for solving fractional-order differential equations using Bernstein Neural Networks (BNNs). The proposed architecture comprises input, hidden, and output layers, where Bernstein polynomials of varying degrees are employed as basis functions. Activation functions are incorporated in the hidden layers to enhance nonlinearity, while the network's output is trained to approximate the solution of the differential equation. The unknown solution is modeled as a function of trainable parameters (weights), which are optimized via the backpropagation algorithm. To evaluate the effectiveness and accuracy of the method, benchmark problems with known exact solutions are considered. Comparative analysis with existing numerical techniques demonstrates that the BNN-based approach yields superior accuracy and computational performance, confirming its potential for efficiently solving complex fractional-order systems.