Innovative Approach to Evaluating the Approximate Solutions Concerning the Fractional Sharma-Tasso-Oliver Equation Comparison

Abstract

In this research, we introduce an improved analytical approximation technique for addressing the time-fractional Sharma-Tasso-Olever problem. To manage nonlinear fractional differential equations that emerge in numerous physical phenomena, we establish an alternative basis for the Laplace Residual Power Series approach (LRPSA). The generalized Taylor series equation and residual functions form the foundation of this strategy. The proposed solution yields positive outcomes. The dependability, efficiency, and simplicity of the suggested method are showcased across all categories of fractional nonlinear problems encountered in technological and scientific domains. Two examples are given to illustrate the effectiveness of the proposed approach in solving various kinds of fractional ordinary differential equations. A comparison with other techniques such as RPS, VIM, HPM reveals that our method produces favourable and efficient results.