Control of chaos in the Burke-Shaw system of fractal-fractional order in the sense of Caputo-Fabrizio

. For the Burke-Shaw system, we propose a fractal-fractional order in the sense of the Caputo-Fabrizio derivative. The proposed system is solved by utilizing the fractal-frac-tional derivative operator with an exponential decay kernel. Time-fractional Caputo-Fabrizio fractal fractional derivatives are applied to the Burke-Shaw-type nonlinear chaotic systems. Based on fixed point theory, it has been demonstrated that a fractal-fractional-order model under the Caputo-Fabrizio operator exists and is unique. Using a numerical power series method, we solve the fractional Burke-Shaw model. Using Newton’s interpolation polynomial, we solve the equation numerically by implementing a novel numerical scheme based on an efficient polynomial.