Today, operators have become the resource of telecommunications data. Therefore, knowledge about subscriptions is easily available for most countries. In recent years, high-speed mobile internet access subscriptions are also increasing rapidly. There are two important subscriptions reviewed by The International Telecommunication Union (ITU): mobile broadband (MBB) subscriptions and Fixed broadband (FBB) subscriptions. In this study, we proposed an original mathematical model employing the fractional analysis theory and evaluate its validity by modeling the mobile broadband and fixed broadband subscriptions of six countries including France, Italy, Turkey, Germany, Spain, and the U.K. Later, we compared the Fractional Model we developed with the Polynomial Model. The results show that the Fractional Model is superior to the conventional Polynomial Model in modeling broadband subscriptions. For all selected countries, our proposed Fractional approach outperforms conventional polynomial regression. For all investigation categories, on average, the fractional approach works better by at least 10% and at most 30%.