Retraction: “A fractional model for predator-prey with omnivore” [Chaos, 29, 013136 (2019)]

The Editor and Publisher of Chaos are retracting the referenced article¹ due to concerns that have been raised regarding the accuracy of the results presented.

In the discussion following Theorem 1 on page 4, the authors claim that the existence and uniqueness of solutions for their model is supported based on work by Losada and Nieto.² However, this reference does not contain a proof that would support such a conclusion.

In addition, the proof of Theorem 3 is incorrect as the equations in (31) do not follow from those in (28) and (29). The source of the error is the use of the following inequality which is not true for all cases:

The condition, $||x(0)||=||ψ1(t)||$⁠, was also used incorrectly.

Finally, the numerical results shown on pages 9–17 cannot be reproduced using the model and given parameters and implementation of the model (as written) will diverge within a few time steps.

The following author has agreed to this retraction:

Abdon Atangana