The Riemann–Liouville fractional derivative for Ambartsumian equation

E. R. El-Zahar; A. M. Alotaibi; A. Ebaid; A. F. Aljohani; J. F. Gómez Aguilar

doi:10.1016/j.rinp.2020.103551

The Riemann–Liouville fractional derivative for Ambartsumian equation

E. R. El-Zahar
, A. M. Alotaibi
, A. Ebaid
, A. F. Aljohani
, J. F. Gómez Aguilar

Mathematics

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

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.

Original language	English
Article number	103551
Journal	Results in Physics
Volume	19
DOIs	https://doi.org/10.1016/j.rinp.2020.103551
State	Published - Dec 2020

Keywords

Ambartsumian equation
Riemann–Liouville
Series solution

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10.1016/j.rinp.2020.103551

Cite this

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title = "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.",

keywords = "Ambartsumian equation, Riemann–Liouville, Series solution",

author = "El-Zahar, \{E. R.\} and Alotaibi, \{A. M.\} and A. Ebaid and Aljohani, \{A. F.\} and \{G{\'o}mez Aguilar\}, \{J. F.\}",

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AU - El-Zahar, E. R.

AU - Alotaibi, A. M.

AU - Ebaid, A.

AU - Aljohani, A. F.

AU - Gómez Aguilar, J. F.

PY - 2020/12

Y1 - 2020/12

N2 - 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.

AB - 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.

KW - Ambartsumian equation

KW - Riemann–Liouville

KW - Series solution

UR - https://www.scopus.com/pages/publications/85097424028

U2 - 10.1016/j.rinp.2020.103551

DO - 10.1016/j.rinp.2020.103551

M3 - Article

AN - SCOPUS:85097424028

SN - 2211-3797

VL - 19

JO - Results in Physics

JF - Results in Physics

M1 - 103551

ER -

The Riemann–Liouville fractional derivative for Ambartsumian equation

Abstract

Keywords

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