The Adomian method applied to some extraordinary differential equations (Q1894227)

The differential equation \(a(x) D^\alpha y + b(x) y = f(x)\) is considered where \(\alpha \in (0,1)\), \(D^\alpha y\) is the Riemann- Liouville fractional derivative of order \(\alpha\); \(a\), \(b\), \(f\) are analytic functions. For \(\alpha = 1/2\) and special functions \(a\), \(b\), and \(f\) the known solutions are obtained by the use of the decomposition method of \textit{G. Adomian} [Nonlinear stochastic operator equations (1986; Zbl 0609.60072)].