If you use maths to describe the world around you — say the growth of a plant, the spread of diseases, or physical forces acting on an object — you soon find yourself dealing with *differential equations*. Differential equations have been an important part of mathematics for centuries. Now there has been a recent surge in *fractional differential equations* as they can be used to model many complex phenomena, from contamination of groundwater, the electrical dynamics of the heart to the design of new materials.

With so many new applications it is an important time to bring the people working in this area together. The Isaac Newton Institute for Mathematical Sciences in Cambridge is currently hosting the *Fractional differential equations* (FDE), bringing interdisciplinary scientists and mathematicians together, including those working on the theoretical side and those finding innovative applications. Find out more about the programme below, including some accessible introductions to the concepts involved to help you explore this growing area of maths.

The calculus of the complex — In this article we find out just what *fractional differential equations* are, and how they can help us understand the world.

The calculus of the complex – the video — In this video from the INI, Dan Aspel speaks to the organisers of the FDE programme about the motivations and potential outcomes of their research programme.

### Background reading

Maths in five minutes: Calculus — Recap your calculus knowledge with our quick introduction.

Maths in a minute: Differential equations — Change is the only constant in our lives – find out why differential equations are so useful for understanding it.

*We produced this collection of content as part of our collaboration with the Isaac Newton Institute for Mathematical Sciences (INI), an international research centre and our neighbour here on the University of Cambridge's maths campus. INI attracts leading mathematical scientists from all over the world, and is open to all. Visit www.newton.ac.uk to find out more.*