WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 25, 2026
Numerical Simulation of Fractional Duffing Problem Using the Ujlayan-Dixit Operator and Adomian Decomposition Method
Authors: , , , , ,
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Abstract: 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.
Keywords:
Fractional calculus, Fractional Duffing Equation, Adomian Decomposition Method (ADM), Ujlayan-Dixit operator, Nonlinear Diffferential Equation, Numerical Simulation
Pages: 386-398
DOI: 10.37394/23206.2026.25.38