Solving Differential Equations of Fractional Order Using Combined Adomian Decomposition Method with Kamal Integral Transformation

Abstract

The differential equation is an equation that involves the derivative (derivatives) of the dependent variable with respect to the independent variable (variables). The derivative represents nothing but a rate of change, and the differential equation helps us present a relationship between the changing quantity with respect to the change in another quantity. The Adomian decomposition method is one of the iterative methods that can be used to solve differential equations, both integer and fractional order, linear or nonlinear, ordinary or partial. This method can be combined with integral transformations, such as Laplace, Sumudu, Natural, Elzaki, Mohand, Kashuri-Fundo, and Kamal. The main objective of this research is to solve differential equations of fractional order using a combination of the Adomian decomposition method with the Kamal integral transformation. Furthermore, the solution of the fractional differential equation using the combined method of the Adomian decomposition method and the Kamal integral transformation was investigated. The main finding of our study shows that the combined method of the Adomian decomposition method and the Kamal integral transformation is very accurate in solving differential equations of fractional order. The present results are original and new for solving differential equations of fractional order. The results attained in this paper confirm the illustrative example has been solved to show the efficiency of the proposed method.