A comparative study of three numerical schemes for solving Atangana–Baleanu fractional integro-differential equation defined in Caputo sense

Abstract

This study contains numerical schemes namely Linear scheme, Quadratic scheme, and Quadratic–linear scheme to solve a fractional integro-differential equation using the Atangana–Baleanu derivative defined in Caputo sense. The error bounds of the schemes are obtained. We discuss four test examples to perform the numerical simulations, and the obtained numerical results ensure that the presented schemes work well and the obtained approximate solution agrees with the analytical solution. The convergence order and maximum absolute errors of the schemes are calculated and their comparative performances are discussed. © 2020, Springer-Verlag London Ltd., part of Springer Nature.