This study presents a new fractional computational approach applied to a new dataset, silicosis. This is a scalable and flexible approach for training neural networks using fractional computation, which conveniently use the conformable fractional derivative. During the training process, the method includes an independent variable, \(\alpha \) , which provides additional degree to the framework. Fractional variants of the sigmoid and relu activation functions are explored and compared to conventional activation functions. This method builds on earlier approaches by employing the conformable fractional derivative. The fractional activation functions notably converge to the actions of their standard version when \(\alpha = 1\) , guaranteeing a smooth integration with conventional neural network models. The study also tackles the problem of managing both positive and negative inputs, which is a crucial prerequisite for the derivative but has been mainly disregarded in earlier studies, underscoring the originality of the current work. The experimental framework incorporates both feedforward neural network and convolutional neural network using fractional activation functions. The findings indicate that the suggested framework performs better and is more accurate for particular values of \(\alpha \) . The efficiency of the suggested computational approach is demonstrated by showing that fractional activation on Convolutional Neural Network when paired with transfer learning, performs better for silicosis chest X-ray classification than conventional transfer learning models.