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Neglecting nonlocality leads to unrealistic numerical scheme for fractional differential equation: Fake and manipulated results.
- Source :
-
Chaos . Jan2019, Vol. 29 Issue 1, pN.PAG-N.PAG. 9p. 13 Graphs. - Publication Year :
- 2019
-
Abstract
- The purpose of this paper is to highlight the main comment raised on the published manuscript [A. Atangana and K. M. Owolabi, Math. Model. Nat. Phenom. 13, 3 (2018)] by Garrappa [Commun. Nonlinear Sci. Numer. Simul. 70, 302–306 (2019)]. It was shown that the scheme proposed by Garrappa [Commun. Nonlinear Sci. Numer. Simul. 70, 302–306 (2019)] did not capture the memory and nonlocality and led to unreliable results. Therefore, we decided to highlight and validate this issue by means of a scheme where misprinting or typos were observed. Further, we propose some examples where some of them were reported by Garrappa [Commun. Nonlinear Sci. Numer. Simul. 70, 302–306 (2019)]. It is shown further by considering different examples of the nature of linear and nonlinear problems, and we show that the scheme presented by Atangana and Owolabi [Math. Model. Nat. Phenom. 13, 3 (2018)] is correct and gives 100% agreement for the case of linear problems with the other methods in the literature, while for the case of nonlinear problems, it gives a reasonable agreement and thus the claim by Garrappa [Commun. Nonlinear Sci. Numer. Simul. 70, 302–306 (2019)] is baseless. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10541500
- Volume :
- 29
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Chaos
- Publication Type :
- Academic Journal
- Accession number :
- 134425351
- Full Text :
- https://doi.org/10.1063/1.5085661