  This paper is concerned with the numerical solution of the third kind
Volterra integral equations with non-smooth solutions based on the recursive
approach of the spectral Tau method. To this end, a new set of the fractional
version of canonical basis polynomials (called FC-polynomials) is introduced.
The approximate polynomial solution (called Tau-solution) is expressed in terms
of FC-polynomials. The fractional structure of Tau-solution allows recovering
the standard degree of accuracy of spectral methods even in the case of
non-smooth solutions. The convergence analysis of the method is studied. The
obtained numerical results show the accuracy and efficiency of the method
compared to other existing methods.
