  The fractional calculus framework will be used to invert the potential energy
function from the classical scattering angle, which will be related to
Riemann-Liouville fractional integral. Numerical solution of this fractional
order problem will be applied to the inverse Rutherford scattering and to the
inverse scattering of Xe--Rn atoms, in which the potential is given by
Lennard-Jones function. Proofs of existence will be presented for more clarity
and completness of the present work. In the two cases considered, the potential
energy function can be retrieved with a desired precision. The present method
gives a clear understanding of the inverse fractional problem framework.
