New Series Solution of the Caputo Fractional Ambartsumian Delay Differential Equationation by Mittag-Leffler Functions

New Series Solution of the Caputo Fractional Ambartsumian Delay Differential Equationation by Mittag-Leffler Functions

The fractional generalization of the Ambartsumian delay equation with Caputo’s fractional derivative is considered. The Ambartsumian delay equation is very difficult to be solved neither in the case of ordinary derivatives nor in the case of fractional derivatives. In this paper we combine the Lapla...

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Main Authors: Weam Alharbi, Snezhana Hristova
Format: Article
Language:English
Published: MDPI AG 2021-01-01
Series:Mathematics
Subjects:
Ambartsumian equation
Caputo fractional derivative
Adomian decomposition method
Laplace-transform
analytic solution
Online Access:https://www.mdpi.com/2227-7390/9/2/157
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spelling doaj-7cf8668d797e4047a67ac3c11e0c19692021-01-14T00:04:28ZengMDPI AGMathematics2227-73902021-01-01915715710.3390/math9020157New Series Solution of the Caputo Fractional Ambartsumian Delay Differential Equationation by Mittag-Leffler FunctionsWeam Alharbi0Snezhana Hristova1Department of Mathematics, Faculty of Sciences, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi ArabiaFaculty of Mathematics and Informatics, Plovdiv University, Tzar Asen 24, 4000 Plovdiv, BulgariaThe fractional generalization of the Ambartsumian delay equation with Caputo’s fractional derivative is considered. The Ambartsumian delay equation is very difficult to be solved neither in the case of ordinary derivatives nor in the case of fractional derivatives. In this paper we combine the Laplace transform with the Adomian decomposition method to solve the studied equation. The exact solution is obtained as a series which terms are expressed by the Mittag-Leffler functions. The advantage of the present approach over the known in the literature ones is discussed.https://www.mdpi.com/2227-7390/9/2/157Ambartsumian equationCaputo fractional derivativeAdomian decomposition methodLaplace-transformanalytic solution
collection DOAJ
language English
format Article
sources DOAJ
author Weam Alharbi
Snezhana Hristova
spellingShingle Weam Alharbi
Snezhana Hristova
New Series Solution of the Caputo Fractional Ambartsumian Delay Differential Equationation by Mittag-Leffler Functions
Mathematics
Ambartsumian equation
Caputo fractional derivative
Adomian decomposition method
Laplace-transform
analytic solution
author_facet Weam Alharbi
Snezhana Hristova
author_sort Weam Alharbi
title New Series Solution of the Caputo Fractional Ambartsumian Delay Differential Equationation by Mittag-Leffler Functions
title_short New Series Solution of the Caputo Fractional Ambartsumian Delay Differential Equationation by Mittag-Leffler Functions
title_full New Series Solution of the Caputo Fractional Ambartsumian Delay Differential Equationation by Mittag-Leffler Functions
title_fullStr New Series Solution of the Caputo Fractional Ambartsumian Delay Differential Equationation by Mittag-Leffler Functions
title_full_unstemmed New Series Solution of the Caputo Fractional Ambartsumian Delay Differential Equationation by Mittag-Leffler Functions
title_sort new series solution of the caputo fractional ambartsumian delay differential equationation by mittag-leffler functions
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2021-01-01
description The fractional generalization of the Ambartsumian delay equation with Caputo’s fractional derivative is considered. The Ambartsumian delay equation is very difficult to be solved neither in the case of ordinary derivatives nor in the case of fractional derivatives. In this paper we combine the Laplace transform with the Adomian decomposition method to solve the studied equation. The exact solution is obtained as a series which terms are expressed by the Mittag-Leffler functions. The advantage of the present approach over the known in the literature ones is discussed.
topic Ambartsumian equation
Caputo fractional derivative
Adomian decomposition method
Laplace-transform
analytic solution
url https://www.mdpi.com/2227-7390/9/2/157
work_keys_str_mv AT weamalharbi newseriessolutionofthecaputofractionalambartsumiandelaydifferentialequationationbymittaglefflerfunctions
AT snezhanahristova newseriessolutionofthecaputofractionalambartsumiandelaydifferentialequationationbymittaglefflerfunctions
_version_ 1724338570897915904

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