Editing Initialized fractional calculus (section)

==Description of initialization==

Working with a properly initialized differ integral is the subject of initialized fractional calculus. If the differ integral is initialized properly, then the hoped-for composition law holds.  The problem is that in differentiation, information is lost, as with ''C'' in the first equation.

However, in fractional calculus, given that the operator has been fractionalized and is thus continuous, an entire '''complementary function''' is needed.  This is called complementary function <math>\Psi</math>.

:<math>\mathbb{D}^q_t f(t) = \frac{1}{\Gamma(n-q)}\frac{d^n}{dt^n}\int_0^t (t-\tau)^{n-q-1}f(\tau)\,d\tau + \Psi(x)</math>