The dynamics of a new chaotic system through the Caputo–Fabrizio and Atanagan–Baleanu fractional operators

Abstract

The aim of this article is to analyze the dynamics of the new chaotic system in the sense of two fractional operators, that is, the Caputo–Fabrizio and the Atangana–Baleanu derivatives. Initially, we consider a new chaotic model and present some of the fundamental properties of the model. Then, we apply the Caputo–Fabrizio derivative and implement a numerical procedure to obtain their graphical results. Further, we consider the same model, apply the Atangana–Baleanu operator, and present their analysis. The Atangana–Baleanu model is used further to present a numerical approach for their solutions. We obtain and discuss the graphical results to each operator in details. Furthermore, we give a comparison of both the operators applied on the new chaotic model in the form of various graphical results by considering many values of the fractional-order parameter [Formula: see text]. We show that at the integer case, both the models (in Caputo–Fabrizio sense and the Atangana–Baleanu sense) give the same results.

Modeling the dynamics of novel coronavirus (2019-nCov) with fractional derivative

“…where q represent the fractional order parameter and D q t is the fractional derivative, the model variables in (13) are nonnegative and has appropriate initial conditions.…”

“…We give a numerical procedure for the solution of the fractional epidemic model (13) by adopting the procedure shown in [15]. The application of this scheme can be seen in many real world problems, see for example [16,17] and the references there in.…”

“…Using the two points lagrange interpolation polynomial for the simplification of the integral in (16), we obtain in the following the numerical scheme for corona virus model (13) given by,…”

“…ð Þ ¼ 50000. Using these initial values and simulated the model (13), we obtain the values of the parameters shown in Table 1, where as the basic reproduction number is estimated R 0 % 2:4829. The data fitting versus model (13) is shown in Fig.…”

“…Research related Atangana-Baleanu derivative and their applications to various models arising in science and engineering can be seen in [4][5][6][7][8]. Some other related papers to the applications of Atangana-Baleanu derivative can be seen in [9][10][11][12][13][14] We consider the reported cases since January 21, 2020 till January 28, 2020, which are higher than the initial days and formulate a mathematical model to parameterize the model. We give brief details about the mathematical modeling of the novel corona virus in Section 2.…”