Conformable fractional derivative grey modelling

The grey modelling in the prediction of time series has been one of the interesting study fields recently due to its efficiency and convenience. Fractional grey models, on the other hand, have become preferable, despite the difficulty in calculations, since they give more effective results than standard models. Difficulties in fractional accumulation and difference calculations have begun to be overcome thanks to new definitions and theorems made in recent years. The new trend in grey modelling is to compose models that are more useful than the previous ones and give results with less error. In this thesis study, three new fractional grey models derived from the conformable fractional order and abbreviated as the OCCFGM(1, 1), ECFGM(1, 1) and FEXGM(1, 1) were created. The results show that these novel models demonstrated a higher predicted accuracy and more robust performance over the other models considered for comparison. In addition, different real applications of the new models were made and the results obtained were interpreted. The optimal values of fractional order were determined by using the Brute-Force approach. The structural parameters of the models were calculated by using the least squares method.