This work is an exposition on computational aspects of principal parts of a vector bundle on projective line over the field of characteristic zero. Principal parts help determine the possibility of algebraically formalizing infinitesimal-neighborhoods of subschemes inside some ambient scheme. The purpose of this study is to look for the possibility of formalizing the algebraic geometric interpretation of fractional derivative. For the latter, this study follows theapproachproposedbyVasilyTarasov. The difference is that Tarasov proposeda geometric interpretation using finite order jet bundles from differential geometry. Present study proposes finite-order principal parts of the structure-sheaf of real projective line as its formal algebraic geometric parallel.