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In this study, the air quality index (AQI) of Indian cities of different tiers is predicted by using the vanilla recurrent neural network (RNN). AQI is used to measure the air quality of any region which is calculated on the basis of the concentration of ground-level ozone, particle pollution, carbon monoxide, and sulphur dioxide in air. Thus, the present air quality of an area is dependent on current weather conditions, vehicle traffic in that area, or anything that increases air pollution. Also, the current air quality is dependent on the climate conditions and industrialization in that area. Thus, the AQI is history-dependent. To capture this dependency, the memory property of fractional derivatives is exploited in this algorithm and the fractional gradient descent algorithm involving Caputo’s derivative has been used in the backpropagation algorithm for training of the RNN. Due to the availability of a large amount of data and high computation support, deep neural networks are capable of giving state-of-the-art results in the time series prediction. But, in this study, the basic vanilla RNN has been chosen to check the effectiveness of fractional derivatives. The AQI and gases affecting AQI prediction results for different cities show that the proposed algorithm leads to higher accuracy. It has been observed that the results of the vanilla RNN with fractional derivatives are comparable to long short-term memory (LSTM).