Spectral Method for Fractional Integral Equations using Jacobi Fractional Polynomials

The authors present a spectral method for solving one-sided linear fractional integral equations on a closed interval that achieves exponentially fast convergence for a variety of equations, including those with irrational order, multiple fractional orders, non-trivial variable coefficients, and initial-boundary conditions. The method uses an orthogonal basis of Jacobi fractional polynomials, which incorporate the algebraic singularities of the solution into the basis functions.