Implementation of Yang residual power series method to solve fractional non-linear systems

In this study, we implemented the Yang residual power series (YRPS) methodology, a unique analytical treatment method, to estimate the solutions of a non-linear system of fractional partial differential equations. The RPS approach and the Yang transform are togethered in the YRPS method. The suggested approach to handle fractional systems is explained along with its application. With fewer calculations and greater accuracy, the limit idea is used to solve it in Yang space to produce the YRPS solution for the proposed systems. The benefit of the new method is that it requires less computation to get a power series form solution, whose coefficients should be established in a series of algebraic steps. Two attractive initial value problems were used to test the technique's applicability and performance. The behaviour of the approximative solutions is numerically and visually discussed, along with the effect of fraction order $\varsigma$. It was observed that the proposed method's approximations and exact solutions were completely in good agreement. The YRPS approach results highlight and show that the approach may be utilized to a variety of fractional models of physical processes easily and with analytical efficiency.