Corrigendum: New numerical approach for fractional differential equations

Abdon Atangana,Kolade M Owolabi,Jordan Hristov,Zakia Hammouch,Gisèle Mophou

doi:10.1051/mmnp/2021039

Abstract

Corrigendum: New numerical approach for fractional differential equations

Highlights

In this paper, we briefly provide some corrections to our previously published article in [1] as pointed out by some anonymous reviewers
In the abstract The sentence, “The Adams-Bashforth method for fractional differentiation suggested and are commonly use in the literature nowadays is not mathematically correct and the method was derived without taking into account the nonlinearity of the power law kernel” The phrase “not mathematically correct” was intended to be “mathematically correct”
The comparison between the numerical and exact solutions is displayed in Figure 1 for different step-sizes and β

Summary

Introduction

We briefly provide some corrections to our previously published article in [1] as pointed out by some anonymous reviewers. The original published article can be accessed online via https://doi.org/10.1051/ mmnp/2018010. In the abstract The sentence, “The Adams-Bashforth method for fractional differentiation suggested and are commonly use in the literature nowadays is not mathematically correct and the method was derived without taking into account the nonlinearity of the power law kernel” The phrase “not mathematically correct” was intended to be “mathematically correct”. 2 Department of Mathematical Sciences, Federal University of Technology, PMB 704, Akure, Ondo State, Nigeria.

Test problem Consider the following Caputo fractional differential equation

Since we assume that