Erdelyi–Kober operator

In mathematics, an Erdélyi–Kober operator is a fractional integration operation introduced by Arthur Erdélyi (1940) and Hermann Kober (1940).

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The Erdélyi–Kober fractional integral is given by

${\displaystyle {\frac {x^{-\nu -\alpha +1}}{\Gamma (\alpha )}}\int _{0}^{x}(t-x)^{\alpha -1}t^{-\alpha -\nu }f(t)dt}$

which generalizes the Riemann fractional integral and the Weyl integral.