The Riemann–Liouville fractional derivative for Ambartsumian equation

Abstract

The Ambartsumian equation, based on the modified Riemann–Liouville fractional derivative, is analyzed in this paper. The solution is expressed as a power series of arbitrary powers and its convergence has been proven. In addition, we show that the present solution reduces to the results in the literature when the fractional derivative tends to 1. Moreover, the behavior of the obtained solution is discussed through figures.