Artificial neural networks have emerged as a strong tool in both science and engineering, particularly in biomedical engineering, giving novel solutions to complex problems across multiple domains. Their ability to learn from data and simulate complex patterns makes them useful in the advancement of technology and scientific knowledge. In this chapter, we propose a single-step Caputo-type fractional technique for solving nonlinear equations. Using local theoretical convergence analysis, the single-step method’s order of convergence is two. To accelerate convergence, a hybrid neural network-based family of single-step techniques is devised. Based on the outcomes of biomedical engineering applications, neural network-based approaches perform better than existing methods in terms of error, CPU time, and iterations.