Adomian Decomposition Method and The Other Integral Transform

The Adomian decomposition method is an iterative method that can be used to solve integral, differential, and integrodifferential equations. The differential equations that can be solved by this method can be of integer or fractional order, ordinary or partial, with initial or boundary value problems, with variable or constant coefficients, linear or nonlinear, homogeneous or nonhomogeneous. This method divides the equation into two forms, namely linear and nonlinear, so that it can solve equations without linearization, discretization, perturbation, or other restrictive assumptions. The basic concept of this method assumes that the solution can be decomposed into an infinite series. This method decomposes the nonlinear form (if any) of the equation with the Adomian polynomial series. This decomposition method can be combined with various integral transform, such as Laplace, Sumudu, Elzaki, and Mohand. The main idea of this technique assumes that the solution can be decomposed into an infinite series, then applies the integral transform to the differential equation. The main advantage of this technique is that the solution can be expressed as an infinite series that converges rapidly to the exact solution. This paper aims to combine the Adomian decomposition method with the new integral transform introduced by Kumar et al. (2022). This integral transform is called the Rishi transform. A scheme for solving fractional ordinary differential equations using the combined method is presented in this paper.