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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

Researcher wins prize for her work to reduce environmental pollution
2016-12-26

Description: Josepha Zielke Tags: Josepha Zielke 

Prof Danie Vermeulen, Dean of the Faculty of Natural
and Agricultural Sciences, and Josepha Zielke, a
PhD student at the Institute for Groundwater studies at the
University of the Free State.
Photo: Leonie Bolleurs

Josepha Zielke, a PhD student at the Institute for Groundwater Studies at the University of the Free State (UFS), received the prize for the best student presentation at the International Mine Water Association (IMWA) symposium in Leipzig, Germany, this year. Her paper was titled Fine Ash Leaching in Tailings Dams – An Impact on the Underlying Aquifers?
 
Zielke said: “It is an honour to receive this prize as a student. IMWA is a big association which allows you to establish a network with other scientists, to exchange opinions and ideas and to gain new inspiration for your own work. It was exciting and informative to hear about the research conducted around the world and to meet the researchers themselves.”
 
Born in Germany, Zielke always wanted to study overseas. During an exchange year in Grade 11, she visited South Africa. When she had to make a decision about in which country to complete her studies, South Africa was first choice as she was familiar with the people and the country.
 
Zielke joins leading institute on groundwater research in the country
She completed her BSc Hons in Geology at the Nelson Mandela Metropolitan University. After working for a year in exploration, she decided to focus her studies on water-related problems which  has been a growing issue, not only in South Africa, but in many places around the world. Zielke heard that the UFS Institute for Groundwater Studies was the leading institute on groundwater research in the country, and decided to join the university.
 
After completing her MSc research, An analysis of the geochemical weathering profile within a fine ash tailings dam, Mpumalanga, South Africa, Zielke started the research for her PhD project on groundwater pollution along a fault system in Mpumalanga.
 
Research adding value to the environment by reducing pollution
She explains the focus of her research: “Several production plants and mine waste facilities are located on or near these geological structures which could be a possible cause of ground and surface water pollution. With the aid of geophysical ground surveys (using electromagnetics and electrical resistivity tomography), aquifer and tracer tests, we are trying to determine where the pollution is coming from, how far it has been distributed and to model the potential risks.
 
“This research will add value to the environment by preventing or at least reducing pollution leaking into the environment. Industrial sites always have a negative footprint on the environment but at least we try and contain it by finding the cause of ground and surface water pollution. Thereafter we try and solve the pollution problem or at least mitigate the damage to prevent the spreading of ground and surface water pollution in the area.”

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