Solution of nonlinear fractional partial differential equations by Shehu transform and Adomian decomposition method (STADM)

Abstract

Several well-known nonlinear partial differential equations (NPDEs) of integer order, including the Heat Equation and the Korteweg–de Vries (KDV) Equation, as well as NPDEs of fractional order, including the fractional advection equation (FAE), fractional gas dynamic equation (FGDE), diffusion equation, and fractional Burger equation (FBE), are approximated analytically in this study using the Shehu Transform Adomian Decomposition Method, which is a combination of two methods, namely, Shehu Transform (ST) and Adomian Decomposition Method (ADM). The Caputo sense is utilized to the fractional derivatives. This semianalytical method is used to acquire the series solutions to several example problems. The main advantage of the approach is that, in contrast to other similar semianalytical methods, it is straightforward to apply. This method has been widely used to answer any class of equations in the sciences and engineering because it can solve a huge class of linear and nonlinear equations effectively, more quickly, and precisely. The obtained solution matches exactly with the solution obtained by other methods.