Conformable fractional calculus will be a promising area of research for information processing as natural language and material modelling due to its ease of implementation. In this paper, we propose a fractional gradient descent method for the backpropagation training of neural networks. In particular, the conformable fractional calculus is employed to evaluate the fractional differential gradient function instead of the classical differential gradient function. The results obtained on a large dataset with this approach provide a new optimized, faster and simpler implemented algorithm than the conventional one.