The Riemann–Liouville fractional derivative for Ambartsumian equation

Results in Physics

A.M. Alotaibi¹  J.F. Gómez Aguilar²  A. Ebaid²  A.F. Aljohani²  E.R. El-Zahar³ 

[1]Department of Basic Engineering Science, Faculty of Engineering, Shebin El-Kom 32511, Menofia University, Egypt

[2]Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia

[3]Department of Mathematics, Faculty of Sciences and Humanities, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia

关键词: Ambartsumian equation;    Riemann–Liouville;    Series solution;   

DOI  :  

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown