Series Solution of System of Fractional Order Ambartsumian Equations: Application in Astronomy

The Ambartsumian equation is arising in astronomy and used in the theory of surface brightness in a milky way. In this paper, we introduce system of fractional order Ambartsumian equations and use the Picard iterative method to obtain the series solution of these equations. The solution is provided in the form of a power series which is convergent for all reals. We prove the convergence of this series.