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 nine-dimensionalLorenz system through Rabotnov fractional-exponential (RFE) kernel fractional derivative. First, derive approximate formula thefractional-order derivative polynomial function $t^{p}$ in terms RFE kernel. work, use spectral collocation method basedon properties shifted Vieta-Lucas polynomials. This procedure converts given model algebraic equations. We satisfy theefficiency and accuracy evaluating residual error function. The results obtained are compared with obtainedby using fourth-order Runge-Kutta method. show that implemented technique is easy efficient tool simulate such models.