Shifted Jacobi-Gauss-collocation with convergence analysis for fractional integro-differential equations

A new shifted Jacobi-Gauss-collocation (SJ-G-C) algorithm is presented for solving numerically several classes of fractional integro-differential equations (FI-DEs), namely Volterra, Fredholm and systems of Volterra FI-DEs, subject to initial and nonlocal boundary conditions. The new SJ-G-C method is also extended for calculating the solution of mixed Volterra-Fredholm FI-DEs. The shifted Jacobi-Gauss points are adopted for collocation nodes and the FI-DEs are reduced to systems of algebraic equations. Error analysis is performed and several numerical examples are given for illustrating the advantages of the new algorithm. (C) 2019 Elsevier B.V. All rights reserved.