For instance, if you define a "Gamma distribution with scale parameter and index " to be the distribution with density on , then you can compute the mean (it is ) and the variance (it is ), so that you must have and .
Solving this, you get and . This answers your question. By the way, the "index" you were given happens to be the "index" of my definition. This could have allowed to find from the only knowledge of the mean.