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Computer-aided diagnosis tools have experienced rapid growth and development in recent years. Among all, deep learning is the most sophisticated and popular tool. In this paper, researchers propose a novel deep learning model and apply it to COVID-19 diagnosis. Our model uses the tool of fractional calculus, which has the potential to improve the performance of gradient methods. To this end, the researcher proposes a fractional-order gradient method for the back-propagation of convolutional neural networks based on the Caputo definition. However, if only the first term of the infinite series of the Caputo definition is used to approximate the fractional-order derivative, the length of the memory is truncated. Therefore, the fractional-order gradient (FGD) method with a fixed memory step and an adjustable number of terms is used to update the weights of the layers. Experiments were performed on the COVIDx dataset to demonstrate fast convergence, good accuracy, and the ability to bypass the local optimal point. We also compared the performance of the developed fractional-order neural networks and Integer-order neural networks. The results confirmed the effectiveness of our proposed model in the diagnosis of COVID-19.