Eur. Phys. J. Plus (2019) 134: 160
https://doi.org/10.1140/epjp/i2019-12565-6

Regular Article

Fractional stochastic modelling illustration with modified Chua attractor

¹ Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South Africa
² Siirt University, Department Mathematics, Faculty of Education, Siirt, Turkey

^* e-mail: AtanganaA@ufs.ac.za

Received: 8 January 2019
Accepted: 7 February 2019
Published online: 17 April 2019

Abstract

Very recently a new concept to capture more complexities in nature was suggested. The concept combines two important concepts of modeling including fractional differentiation and stochastic approach. In this work, we aim to investigate new chaotic attractors using the modified Chuan models and the new approach. We use the log-normal distribution to convert constant parameters into distribution. Then we use 3 different types of differential operators including Caputo, Caputo-Fabrizio and Atangana-Baleanu derivatives. We solve the new equations by using the newly introduced numerical scheme. Our numerical simulations display very new attractors.