Numerical treatment for a nine-dimensional chaotic Lorenz model with the Rabotnov fractional-exponential kernel fractional derivative

In this paper, we will present an effective simulation to study the solution behavior of a high dimensional chaos by considering the nine-dimensionalLorenz system through the Rabotnov fractional-exponential (RFE) kernel fractional derivative. First, we derive an approximate formula of thefractional-order derivative of a polynomial function $t^{p}$ in terms of the RFE kernel. In this work, we use the spectral collocation method basedon the properties of the shifted Vieta-Lucas polynomials. This procedure converts the given model to a system of algebraic equations. We satisfy theefficiency and the accuracy of the given procedure by evaluating the residual error function. The results obtained are compared with the results obtainedby using the fourth-order Runge-Kutta method. The results show that the implemented technique is easy and efficient tool to simulate the solution of such models.