Improving urban growth models with fractional calculus

17 Oct 2022 Science, Mathematics and Technology Complex Engineering Systems

Article by Ashley Piccone as featured on AIP Publishing.

SUTD - Chun Yun Kee, Cherq Chua, and  L. K. Ang
Information Technology University of the Punjab - Muhammad Zubair

The mathematical tool accounts for complex systems where changes do not occur instantaneously, making it more suitable for studying cities.

Urban growth models can analyze and predict the attributes of a city as a function of population. They provide a better knowledge base for infrastructure development, transportation planning, and resource allocation and consumption.

This information is crucial for sustainable city management, as the population in urban areas is expected to increase from 55% to 68% by 2050.

Kee et al. expanded on existing urban growth models by incorporating fractional calculus, which accounts for more complexity.

“In our paper, we assume cities have memory effects: their response to change is not instantaneous in time,” said author Ricky L. K. Ang. “This time-lapsed effect is formulated under fractional calculus, which provides another parameter that can be used to explain the empirical data better.”

Using publicly available data from many countries, the team found that the new model shows better agreement than traditional alternatives for some urban attributes, such as congestion delay, water supply, and electricity consumption. They hope to develop a platform where others can use the model while maintaining data privacy.

“The interaction among people will likely play a key part in a city’s socioeconomical dynamics, in terms of innovation, prosperity, and sustainability,” said Ang. “Modeling, characterizing, and predicting the future development of cities under the challenges of climate change — in both high- and low-income nations — is an important problem.”

The researchers plan to improve the model to study non-linear memory effects due to the interactions between cities. They are also interested in exploring the reasons why some specific urban attributes are beneficial due to the embedded memory effects.

Source: “Fractional modeling of urban growth with memory effects,” by Chun Yun Kee, Cherq Chua, Muhammad Zubair, and L. K. Ang, Chaos (2022). The article can be accessed at