Advanced Mathematical Models & Applications

An optimization technique for approximate analytical equations is presented in this study, it is a different using for the Ezaki residual power series method (ERPS) to solve non- holonomic system problems that occur in a variety of physical phenomena. This method is based on the extended Taylor series formulation and the residue function. The positive results of the proposed methods have been shown that, it has been proven to be reliable, efficient and easy to use for solving all kinds of fractional non- holonomic system problems using Caputo derivative in technical and analytical fields. Moreover, our methodology has been shown positive and efficient results when compared with existing methods such as LRPS.