Fractional Study of the Non-Linear Burgers’ Equations via a Semi-Analytical Technique

Abstract

Most complex physical phenomena are described by non-linear Burgers’ equations, which help us understand them better. This article uses the transformation and the fractional Taylor’s formula to find approximate solutions for non-linear fractional-order partial differential equations. Solving non-linear Burgers’ equations with the right starting data shows that the method utilized is correct and can be utilized. Based on the limit of the idea, a rapid convergence McLaurin series is used to obtain close series solutions for both models with less work and more accuracy. To see how time-Caputo fractional derivatives affect how the results of the above models behave, in three dimension figures are drawn. The results showed that the proposed method is an easy, flexible, and helpful way to solve and understand a wide range of non-linear physical models.

Keywords

• fractional non-linear Burgers’ equations
• caputo operator
• residual power series transform method
• analytical solution