What is "differintegral"

In fractional calculus, an area of applied mathematics, the differintegral is a combined differentiation/ integration operator. Applied to a function ƒ, the q-differintegral of f, here denoted by

Df
is the fractional derivative (if q > 0) or fractional integral (if q < 0). If q = 0, then the q-th differintegral of a function is the function itself. In the context of fractional integration and differentiation, there are several legitimate definitions of the differintegral.