In mathematics, an Erdélyi–Kober operator is a fractional integration operation introduced by and .
The Erdélyi–Kober fractional integral is given by
| x-\nu-\alpha+1 | |
| \Gamma(\alpha) |
| x | |
| \int | |
| 0 |
(t-x)\alpha-1t-\alpha-\nuf(t)dt
which generalizes the Riemann fractional integral and the Weyl integral.