Numerical Simulation of Fractional Duffing Problem Using the Ujlayan-Dixit Operator and Adomian Decomposition Method

This paper proposes a generalized computational framework for solving the fractional Duffing equation based on the Adomian Decomposition Method combined with the Ujlayan–Dixit operator. A novel generalized formulation for repeated fractional differentiation is derived, leading to an efficient iterative solution scheme. The proposed approach is applied to different cases of the Duffing system, and its accuracy and convergence behavior are systematically evaluated through comparison with the Runge–Kutta fourth-order method. Furthermore, the influence of the fractional order on the system dynamics is analyzed. The results demonstrate that the proposed method provides accurate, stable, and computationally efficient solutions, highlighting its potential for solving nonlinear fractional differential equations.