Multi-term fractional differential equations, multi-order fractional differential systems and their numerical solution

Fractional differential equations containing only one fractional derivative are a well understood and frequently used tool for the mathematical description of many physical processes, but they are not always sufficient to reflect all the relevant phenomena. It is sometimes necessary to use models with more than one fractional derivative. We describe two important mathematical ways to use this concept: multi-term equations and multi-order systems. First we show the relations between these two concepts. Then we investigate their most important analytical properties, and finally we look at numerical methods for their approximate solution. © 2008 Lavoisier, Paris.