Numerical Approximation of Fractional Relaxation-Oscillation Equation by Aboodh Transform Method

In this paper, we present the approximate solutions of fractional relaxation-oscillation equations by using Aboodh Transform Method (ATM). Some examples are considered to illustrate the capability and reliability of the method. The solutions obtained are presented in the form of rapidly convergent series with easily computable terms. The results obtained by ATM are compared with the exact solutions, the solutions obtained by Iterative Decomposition Method (IDM), Optimal Homotopy Asymptotic Method (OHAM) and Generalized Taylor Matrix Method (GTM). The result revealed that the solutions obtained by ATM which is found to be exactly the same as the solution obtained by IDM are in good agreement with the known exact solutions and solution obtained by OHAM, GTM. The applicability, reliability and effectiveness of the proposed method are tested on three examples and results show that the proposed method is more effective and convenient to use and its high accuracy is evident.