Applications of the ARA-Residual Power Series Technique to Physical Phenomena

Abstract

In this paper, a new analytical method called the ARA-Residual power series method (ARA- RPSM) is implemented to solve some fractional physical equations. The methodology of the proposed method based on applying the ARA-transform to the given fractional differential equations, followed by the creation of approximate series solutions using Taylor’s expansion. Then the series solution is transformed using the inverse of the ARA-transform to get the solution in the original space. Accuracy, effectiveness, and validity of the suggested method are demonstrated through the discussion of three attractive applications. The solution obtained using ARA-RPSM demonstrates good agreement when compared to the solutions found using other methods.