“…With a priori knowledge of the singularity of the underlying solution, such a tool can provide very accurate approximation to a large class of singular problems with suitable choices of { k } (see, e.g., [2,35,36]). Recently, Shen and Wang [43] associated the Müntz polynomials with Jacobi polynomials and developed efficient and accurate Müntz-Galerkin methods for some singular problems with typical singularities of the type: k = k with ∈ (0, 1). Hou and Xu [17] further studied the so-called factional Jacobi polynomials: J , , n (x) = J , n (2x − 1) for x ∈ (0, 1), , > −1 and > 0, with applications to the integral-differential and fractional differential equations.…”