The Riemann–Liouville fractional derivative for Ambartsumian equation
Essam R. El‐Zahar, Abeer M. Alotaibi, Abdelhalim Ebaid, A. F. Aljohani, J. F. Gómez‐Aguilar
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.
Topics & Concepts
Derivative (finance)Fractional calculusConvergence (economics)MathematicsPower seriesSeries (stratigraphy)Mathematical analysisRiemann hypothesisApplied mathematicsMathematical physicsPaleontologyFinancial economicsEconomic growthEconomicsBiologyFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsNonlinear Differential Equations Analysis