Analysis of non-equilibrium 4D dynamical system with fractal fractional Mittag–Leffler kernel

Abstract

In this article, we presents the theoretical and numerical study of the four dimensional chaotic system which has no equilibrium point in the sense of fractal-fractional Mittag–Leffler kernel. By using the approach of fixed point theory, the existence and uniqueness of solution for the considered model is studied. The approximate solution is acquired by applying the technique of fractional Newton’s polynomial interpolation. The numerical simulations of the approximate results are presented for different fractal dimension and fractional orders. From the figures we obtained the butterfly-type attractor by using different values of fractal dimension which shows symmetric form. Furthermore, fractal and fractional operators show significant impacts on the dynamics of the non-linear chaotic systems.

Keywords

• 4D chaotic system
• Fractal-fractional operator
• Existence and uniqueness
• Numerical solution