Solution of Ambartsumian Delay Differential Equation with Conformable Derivative

Sayed M. Khaled, Essam R. El-Zahar and Abdelhalim Ebaid
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Sayed M. Khaled: Department of Studies and Basic Sciences, Faculty of Community, University of Tabuk, Tabuk 71491, Saudi Arabia
Essam R. El-Zahar: Department of Mathematics, College of Sciences and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-kharj 11942, Saudi Arabia
Abdelhalim Ebaid: Department of Studies and Basic Sciences, Faculty of Community, University of Tabuk, Tabuk 71491, Saudi Arabia

Mathematics, 2019, vol. 7, issue 5, 1-10

Abstract: This paper addresses the modelling of Ambartsumian equation using the conformable derivative as an application of the theory of surface brightness in astronomy. The homotopy perturbationmethod is applied to solve this model, where the approximate solution is given in terms of the conformable derivative order and the exponential functions. The present solution reduces to the corresponding one in the relevant literature as a special case. Moreover, a rapid rate of convergence has been achieved for the obtained approximate solutions. Furthermore, the accuracy of the obtained numerical results is validated via calculating the residual against the impeded parameters. It is shown graphically that the obtained residual approaches zero in various cases, which proves the efficiency of the current analysis.

Keywords: Ambartsumian equation; conformable derivative; homotopy perturbation method; series solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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