Discussing a Solution to Nonlinear Duffing Oscillator with Fractional Derivatives Using Homotopy Analysis Method (HAM) | Chapter 5 | Theory and Practices of Mathematics and Computer Science Vol. 6

In this paper, we obtain an empirical solution to the original valued fractional order derivative problem of the Duffing oscillator. The Homotopy Analysis Method (HAM) was used to achieve the analytical solution to the initially valued problem proposed. The problem was first translated to its augmented equivalent set of equations having the same order in order to achieve our objective. An example showed the precision of the result obtained and the solution was demonstrated graphically. For the excitation amplitude λ and the excitation frequency, it has been found that the amplitude often increases as they rise. It has been noted that the system becomes more unstable as the time unit increases, and this behavior is not out of place.

Aurthor(s) Details:

C. L. Ejikeme
Department of Mathematics, University of Nigeria, Nsukka, Nigeria.

M. O. Oyesanya
Department of Mathematics, University of Nigeria, Nsukka, Nigeria.

D. F. Agbebaku
Department of Mathematics, University of Nigeria, Nsukka, Nigeria.

M. B. Okofu
Department of Mathematics, University of Nigeria, Nsukka, Nigeria.

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