Application of Fractal-Fractional Operators to Study a Lorenz Model

This paper will extend a straight forward system of nonlinear equations to the realm of fractal-fractional nonlinear systems and conduct a numerical analysis of the results. This paper present the fractal-fractional dynamics of a Lorenz model. Initially, we formulate the model and suggest some values for the parameters and initial conditions to show the model become chaotic. Then we apply the fractal-fractional operators in the sense of Caputo on the given model. For the fractal-fractional model in each operator, a novel numerical approach is presented. Some suitable values for the fractal and fractional orders are considered, and the graphical results are shown.