The contemporary application of artificial neural network (ANN) has transcended traditional computer science problems, making significant inroads into the field of mathematics. A notable variant, the feedforward neural network (FNN), has emerged as a powerful tool for approximating solutions to fractional differential equations (FDEs). However, researchers have often limited themselves to ANN with a single hidden layer. Recent advancements in various real-world applications have demonstrated the superior performance achieved by incorporating multiple hidden layers. This study focuses on investigating the accuracy of Caputo-Fabrizio FDEs (CFFDEs) by extending the hidden layers in feedforward ANN from one to two, resulting an extended feedforward neural network (EFNN). At first stage, the method formulation involving type of CFFDEs, construction of approximation solution and approximation of Caputo- Fabrizio derivative is derived. Then, the vectorization is implemented for forward propagation, approximate solution and error function. In the last stage, the learning solver that use Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is described. The effectiveness of the EFNN-BFGS approach is validated through several CFFDEs, including a practical application to tumor-immune dynamics. Numerical results demonstrate that the proposed scheme offers improved accuracy and outperforms existing methods.