Complexity
July/August 2016 Volume 21, Issue 6 Pages 1–459
http://onlinelibrary.wiley.com/doi/10.1002/cplx.v21.6/issuetoc

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Research Articles
Modeling the spread of Rubella disease using the concept of with local derivative with fractional parameter : Beta-Derivative (pages 442–451)
Abdon Atangana and Badr Saad T. Alkahtani
Version of Record online: 10 JUN 2015 | DOI: 10.1002/cplx.21704
Abstract
Our aim in this work was to examine the model underpinning the spread of the Rubella virus using the novel derivative called beta-derivative. The study of the equilibrium points together with the analysis of the disease free equilibrium points was presented. Due to the complexity of the modified equation, we introduced a new operator based on the Sumudu transform. The properties of this operator were proposed and proved in detail. We made used of this operator together with the idea of perturbation method to derive a special solution of the extended model. The stability of the method for solving this model was presented. The uniqueness of the special solution was presented, and numerical simulations were done. The graphical representations show that the model depends on both parameters and the fractional order.