Accuracy estimation of the approximated Atangana-Baleanu operator

In the paper, the accuracy analysis of the approximation of the Atangana-Baleanu (AB) operator is presented. The AB operator is the nonsingular kernel operator proposed by Atangana and Baleanu. It is obtained by replacing the exponential function in the Caputo-Fabrizio operator by the Mittag-Leffler function. The Laplace transform of the AB operator requires approximating the factor sa. This is done using the well-known Oustaloup Recursive Approximaion (ORA) approximation. The step and frequency responses of the approximation are compared to the analytical responses. As the cost function, the FIT function available in MATLAB was applied. Results of simulations show that the use of ORA allows us to obtain the accurate approximant of the AB operator.