Solution of an Extraordinary Differential Equation by Adomian Decomposition Method

Large classes of linear and nonlinear differential equations, both ordinary as well as partial, can be solved by the Adomian decomposition method [3, 4, 6]. This method is much more simpler in computation and quicker in convergence than any other method available in the open literature. The application of the fractional differential equation in physical problems is available in the book of Bracewell [11]. Recently, the solution of the fractional differential equation has been obtained through the Adomian decomposition method by the researchers in [7, 14]. In this paper, we solve a differential equation containing a fractional derivative of order half along with an ordinary first-order derivative using the Adomian decomposition method. Then the solution obtained by this method is verified with that of the transformed ordinary differential equation derived from the original fractional differential equation. For the sake of convenience, we first of all give definitions of fractional integral and fractional derivative introduced by Riemann-Liouville as discussed in [18, 20, 21].