Fractional pseudospectral integration matrices for solving fractional differential, integral, and integro-differential equations

Abstract

The main purpose of this work is to provide fractional pseudospectral integration matrices (FPIMs) and apply them to solve fractional differential, integral, and integro-differential equations. In order to achieve this goal, we present exact approaches to compute FPIMs and efficient and stable ways to calculate the associated Lagrange interpolating polynomials. Subsequently, the applications of FPIMs to fractional differential, integral, and integro-differential equations are described in detail. Finally, we provide a rigorous convergence analysis for the Jacobi-type pseudospectral scheme via a linear fractional integral equation, which indicates the approximation errors in both L∞ and Lω(α,β)2 spaces decay exponentially for −1<α,β≤0. Numerical results on benchmark fractional integro-differential equations demonstrate the performance of the proposed methods.