  In this work we show that it is possible to calculate the fractional
integrals and derivatives of order $\alpha$ (using the Riemann-Liouville
formulation) of power functions $\left( t-\ast\right) ^{\beta}$ with $\beta$
being any real value, so long as one pays attention to the proper choosing of
the lower and upper limits according to the original function's domain. We,
therefore, obtain valid expressions that are described in terms of function
series of the type $\left( t-\ast\right) ^{\pm\alpha+k}$ and we also show that
they are related to the famous hypergeometric functions of the
Mathematical-Physics.
