A Series Approximate Solution to the Fractional Relaxation Oscillation Equations

It is well known that analytical methods for nonlinear differential equations are only available for a few numbers of problems. In this paper, we will solve the fractional relaxation oscillation equation using the Laplace Residual Power Series Method (LRPSM). The relaxation oscillator problem helps in understanding many phenomena that occur in chemical, physical, and biological processes. The advantages of RPSM are that it is easy to apply and it gives a fast-converging series solution in a faster and effortless manner compared to the residual power series (RPS) method. Numerical and graphical results are covered with different values of α to demonstrate the efficiency and capabilities of the presented method.