GENERALIZED SOLUTIONS OF FRACTIONAL BURGER’S EQUATION AND RATIONAL PHYSICAL SYSTEMS VIA A NEOTERIC ALGORITHM

In this paper, we propose a novel approach coupled with the iteration method. This procedure is obtained by combining the Natural Transform Method and the Residual Power Series Method into a new iteration procedure named the Natural Transform Residual Power Series Method (NTRPSM). The novelty of this study is to obtain general solutions to the fractional Burger’s equation and rational physical systems using the NTRPSM. The results obtained via the present method are a generalization of the Laplace transform residual energy series method (LTRPSM), and the Sumudu transform residual energy series method (STRPSM). We study Burger’s equation, which is one of the best equations in fluid mechanics used in various fields, such as acoustics, continuous stochastic processes, and dispersive water. Also, we study fractional physical systems because they have received considerable attention in the study of shallow water waves, etc. The outcomes demonstrated the simplicity, quality, and commonness of the NTRPSM.