A Numerical Study for Fractional Problems with Nonlinear Phenomena in Physics

In this paper, we investigate the solution of fractional Duffing equation. This problem is important since it appears in a variety of science models, including engineering, biology, and physics. The fractional derivative will give us the chance to consider the history of the displacement function in the interval [0, t]. A numerical solution of fractional problems with strongly oscillators is investigated. The spline spaces are used to approximate the solution. It is worth mentioning that the standard basis such as polynomials will not work with this type of problems since there are strong oscillators. To show the validity of our results, we compare them with four different methods which are HPM, MHPM, SHPM, and collocation method using polynomials as basis for the approximate solution. The error in our approximation is 10^-10 comparing with other methods which are of 10^-6 or more. The numerical results reveal that our results are accurate and the proposed method can be used for other physical problems.