## ABSTRACT

In this chapter, we first introduce fractional calculus (i.e., fractional integration and fractional diﬀerentiation). Generally speaking, the fractional integral mainly means (fractional) Riemann-Liouville integral. The fractional derivatives consist of at least six kinds of definitions, but they are not equivalent. Here, we present the most frequently used fractional integral and derivatives, i.e., the Riemann-Liouville integral, the Riemann-Liouville derivative, the Caputo derivative, etc. Then we study their important properties, some of which are easily confused. Besides, we further introduce the definite conditions of fractional diﬀerential equations which are often misused.