New Series Solution of the Caputo Fractional Ambartsumian Delay Differential Equationation by Mittag-Leffler Functions

The fractional generalization of the Ambartsumian delay equation with Caputo’s derivative is considered. very difficult to be solved neither in case ordinary derivatives nor derivatives. In this paper we combine Laplace transform Adomian decomposition method solve studied equation. exact solution obtained as a series which terms are expressed by Mittag-Leffler functions. advantage present approach over known literature ones discussed.