  We calculate the fractional integral and derivative of the potential $1/r$
for all values of the fractional order $-1< \alpha \leq 0$ and $\alpha\geq 0$.
We show that the result has the same form for all values of $\alpha$.
Applications can be implemented to discuss deformed potential fields resulting
from fractional mass or charge densities in gravity and electrostatics
problems. The result can also be applied to modify the inverse-quare law
gravity as predicted by new physics.
