An innovative analytical method utilizing aboodh residual power series for solving the time-fractional newell-whitehead-segel equation

In this study, we use a new method called Abode Residual Power Series Method (ARPSM) to derive the analytical results of the Newell-Whitehead-Siegel equation. The Newell-Whitehead-Segel equation is an important model used in biology, finance, fluid mechanics, and various other processes. The fractional derivative in this equation is considered in the Caputo sense. This method combines the Aboodh transform with the Residual Power Series Method (RPSM). One of the key advantages of our approach is that the Aboodh transformation operator converts the fractional differential equation into an algebraic equation, thereby significantly reducing the computational effort required in the subsequent algebraic steps. A primary feature of our proposed method is its simplicity in computing the coefficients of terms in a series solution using the straightforward concept of limits at infinity. The effectiveness of the proposed approach is demonstrated through graphical and numerical data. Based on our findings, we conclude that our approach is both straightforward to implement and accurate.