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07 September 2018 Photo Stephen Collett
Mathematician makes popular contribution to science Prof Atangana
Prof Atangana is the first African under 40 years of age to be selected as African Academic of Science affiliated in Mathematics. He recently delivered his inaugural lecture and is pictured with Eelco Lukas, Director of the Institute for GroundwaterStudies at the UFS (middle) and Prof Hendri Kroukamp, Acting Vice-Rector: Academic
Prof Abdon Atangana, researcher in the Institute for Groundwater Studies at the University of the Free State (UFS), recently delivered his inaugural lecture on the topic: Understanding God’s Nature with Non-Local Operators.

His research interests are methods and applications of partial and ordinary differential equations, fractional differential equations, perturbation methods, asymptotic methods, iterative methods, and groundwater modelling. Prof Atangana is the founder of the fractional calculus with non-local and non-singular kernels popular in applied mathematics today. He has introduced more than 12 mathematical operators, most of which bear his name (such as the Atangana-Baleanu fractional integral).

He stated: “We will not stop until we change the classical view of doing mathematics. Mathematics is not a subject but a tool given to mankind by God to understand nature. One single mathematical operator cannot portray God’s nature accurately. Therefore the Atangana Baleanu was suggested.”

New weapons

Most physical problems can be expressed in terms of mathematical formulations called differential equations. According to him the differential equation’s aim is to analyse, understand, and predict the future of a physical problem. Prof Atangana introduced the Atangana-Baleanu fractional integral. This brought new weapons into applied mathematics to model complex real-world problems more accurately.

Prof Atangana explained: “The Atangana-Baleanu fractional derivative is able to describe real-world problems with different scales, or problems that change their properties during time and space for instance, the spread of cancer, the flow of water within heterogeneous aquifers, movement of pollution within fractured aquifers, and many others. This crossover behaviour is observed in many empirical systems.”

Sudden change

The Atangana-Baleanu fractional derivative is also able to describe physical or biological phenomena, such as a heart attack, the physiological progression from life to death, structural failure in an aeroplane, and many other physical occurrences with sudden change with no steady state.

The new differential and integral operators are nowadays in fashion and are being applied with great success in many fields to model complex natural phenomena. It is believed that the future of modelling complex real-world problems relies on these non-local operators.

News Archive

Groundwater management vital for groundwater sustainability
2016-11-09

Description: Dr Yolanda Kotzé Tags: Dr Yolanda Kotzé

Dr Yolanda Kotzé, Affiliated Researcher in the
UFS Institute for Groundwater Studies, is passionate
about the management of groundwater.
Photo: Rulanzen Martin

An interest in groundwater resource management ignited the spark for a PhD research thesis by Dr Yolanda Kotzé, Affiliated Researcher in the Institute for Groundwater Studies (IGS) at the University of the Free State (UFS).

Her PhD research thesis titled, A Framework for Groundwater Use Authorisations as Part of Groundwater Governance in Water Scarce Areas within South Africa, was the result of her interest in groundwater resource management. Dr Kotzé identified the agricultural sector as one of the major water users, and a decision was made to conduct research within this sector.  

Research funded by Institute for Groundwater Studies
Groundwater is water found underground in cracks and spaces in soil, sand, and rocks. It is stored in, and moves slowly through geological formations of soil, sand, and rocks (aquifers). The National Department of Water and Sanitation was indirectly the client for this research. The research project was funded by the IGS. Given the current drought, effective groundwater resource management can be achieved within all sectors through sustainable abstraction and use without over-abstraction.

“Groundwater can be effectively managed
in the agricultural sector by sustainable use,
monitoring the quantity of groundwater use,
and measuring groundwater levels,”
said Dr Kotzé.

Research addresses improvement of groundwater management
Her promotor, mentor, teacher, and friend, the late Prof Gerrit van Tonder, introduced her to the field of Geohydrology, and especially to groundwater resource management. “With my research, I made a significant contribution to the improvement of groundwater governance and groundwater resource management, as well as to the handling of groundwater use authorisations for irrigation purposes in South Africa,” said Dr Kotzé. With this significant contribution, she attempts to address the phenomenon of poor groundwater allocation and groundwater resource management by means of a framework. The development of this framework has shown the value of action research in an attempt to find a solution to a problem. “Groundwater can be effectively managed in the agricultural sector by sustainable use, monitoring the quantity of groundwater use, and measuring groundwater levels,” said Dr Kotzé.

The methodology of the research consisted primarily of action research, which has a five-phase cyclical process. The research was Dr Kotzé’s application for a PhD in Geohydrology at the UFS in 2012. The research was completed in 2015.

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