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Development of analytical solution for a generalized Ambartsumian equation

Based on the conformable derivative, a generalized model of the Ambartsumian equation is analyzed in this paper. The solution is expressed as a power series of arbitrary powers. In addition, the convergence of the obtained series solution is theoretically proven. Furthermore, it is shown that the current series reduces to the corresponding one in the literature as the conformable derivative tends to one. It is also revealed that the obtained results are of acceptable accuracy. It is found that the residuals tend to zero in specific sub-domains. The diagonal Pade approximants are implemented to extend the domain of converge to include the whole domain.