A computationally efficient fractional predictor corrector approach involving the Mittag Leffler kernel

TL;DR

This paper introduces a new predictor-corrector numerical scheme based on Newton interpolation for solving fractional differential equations with Mittag-Leffler kernels, demonstrating improved accuracy and efficiency.

Contribution

It presents a novel predictor-corrector method utilizing piecewise quadratic Newton interpolation for fractional derivatives involving Mittag-Leffler functions.

Findings

The scheme effectively solves fractional differential equations with Atangana-Baleanu derivatives.

Numerical experiments show significant accuracy improvements over existing methods.

The approach is computationally efficient for nonlinear fractional problems.

Abstract

In this paper, based on Newton interpolation we have proposed a numerical scheme of predictor-corrector type in order to solve fractional differential equations with the fractional derivative involving the Mittag-Leffler function. We have added an auxiliary midpoint in each sub-interval, this allows us to use a piecewise quadratic Newton interpolation to derive the corrector scheme. The derivation of the schemes for the midpoint and the predictor is done by means of a piecewise linear Newton interpolation. We present some illustrative examples for initial value problems that involve fractional derivatives in the sense of Atangana-Baleanu. The results of numerical experiments show that the proposed scheme is a powerful technique to handle fractional differential equations with nonlinear terms that involve operators of Atangana-Baleanu type. Moreover, the proposed method significantly improves the numerical accuracy in comparison with other methods.