Stability of Fractional Order System of Duffing Equation with Quadratic and Cubic Nonlinearities

Authors

  • Selvam AG Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur-635601, Vellore Dist., Tamil Nadu, India
  • Vignesh D Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur-635601, Vellore Dist., Tamil Nadu, India
  • Janagaraj R Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur-635601, Vellore Dist., Tamil Nadu, India

Keywords:

Duffing equation, Fractional order system, Stability Nonlinear system

Abstract

In physics, mechanics and engineering, Duffing equations are used in describing the oscillatory systems with non linearities and is famous in study of nonlinear dynamics. Here, we study the asymptotic stability of the fractional order unforced damped Duffing equation with quadratic nonlinearity. Local asymptotic stability conditions for commensurate order fractional derivative system with order lying in is discussed without considering integer order. The stability of the system is investigated with fractional orders in two ranges (0,1) and (1,2). For different values of the parameters, examples with simulations are performed. Sensitivity of the system for the small variation in fractional order is analyzed with 2-Dimensional time plots. Lyapunov exponents for the system is investigated with plots and values of Lyapunov exponents are tabulated

References

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Published

2025-11-25

How to Cite

[1]
A. G. M. Selvam, D. Vignesh, and R. Janagaraj, “Stability of Fractional Order System of Duffing Equation with Quadratic and Cubic Nonlinearities”, Int. J. Comp. Sci. Eng., vol. 7, no. 5, pp. 16–19, Nov. 2025.

Issue

Vol. 7 No. 5 (2019): IJCSE Special Issue Mar Edition

Section

Research Article

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