The Riemann–Liouville fractional derivative for Ambartsumian equation

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 liter...

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Bibliographic Details
Published inResults in physics Vol. 19; p. 103551
Main Authors El-Zahar, E.R., Alotaibi, A.M., Ebaid, A., Aljohani, A.F., Gómez Aguilar, J.F.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2020
Elsevier
Subjects
Ambartsumian equation
Riemann–Liouville
Series solution
Riemann–Liouville
Ambartsumian equation
Series solution
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Summary: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. •The Ambartsumian equation, based on the modified Riemann–Liouville fractional derivative is analyzed in this paper.•New complex dynamics are obtained with the application of this fractional derivative.•The solution is expressed as a power series of arbitrary powers and its convergence has been proven.
ISSN:2211-3797
2211-3797
DOI:10.1016/j.rinp.2020.103551