In this paper, the newly developed fractal-fractional differential and integral operators are used to analyze the dynamics of chaotic system based on image encryption. The problem is modeled in terms of classical order nonlinear, coupled ordinary differential equations that are then generalized through fractal-fractional differential operator of Mittag-Leffler kernel. In addition to that, some theoretical analyses, such as model equilibria, existence, and uniqueness of the solutions, have been proved. Furthermore, the highly non-linear problem is solved by adopting a numerical scheme through MATLAB software. The graphical solution is portrayed through 2D and 3D portraits. Some interesting results are concluded considering the variation of fractional-order parameter and fractal dimension parameter.