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

•A new shifted Jacobi–Gauss-collocation algorithm is presented.•Different classes of fractional integro-differential equations are addressed.•Error analysis is performed.•Numerical examples are given for illustrating the method advantages. 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.