Solution of Ambartsumian Delay Differential Equation in the q-Calculus

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Abdulaziz M. Alanazi, Abdelhalim Ebaid


The Ambartsumian equation in view of the q-calculus is investigated in this paper. This equation is of practical interest in the theory of surface brightness in the Milky Way. Two approaches are applied to obtain the closed form solution. The first approach implements a direct series assumption while the second approach is based on the Adomian decomposition method. The two approaches lead to a unique power series of arbitrary powers. Furthermore, the convergence of the obtained series is theoretically proven. In addition, we showed that the present solution reduces to the results in the relevant literature when the quantum calculus parameter tends to 1.

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