In this study, we present a modified analytical approximation method to find the time-fractional Sharma-Tasso-Olever issue solving. In order to tackle nonlinear fractional differential equations that arise in a variety of physical processes, we begin by providing an alternate foundation for the Laplace Residual Power Series Technique (LRPSM). Thus, the generalized Taylor series equation and residual functions serve as the foundation for this approach.

More precisely, our approach and the suggested solution produce good results. Moreover, the reliability, effectiveness, and simplicity of this approach are demonstrated for all classes of fractional nonlinear issues that arise in technological and scientific fields. Two examples are provided to exemplify how the considered scheme works in calculating various types of fractional ordinary differential equations. Finally, the obtained results in this article are compared with other methods such as Residual Power Series (RPS), Variational Iteration Method (VIM), and Homotopy Perpetration Method (HPM). The consequences of our method are good and effective.