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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2021, Volume 24, Number 4, Pages 365–382
DOI: https://doi.org/10.15372/SJNM20210401 (Mi sjvm786) 		 
On an integro-differential fractional nonlinear Volterra-Caputo equation

S. Guemara, H. Guebbaib, S. Lemitac

a Université Yahia Fares Médéa, Pôle urbain, Médéa, Algerie
b Laboratoire des Mathématiques Appliquées et de Modélisation, Université 8 Mai 1945, Guelma, Guelma, Algérie
c Ecole Normale Supérieure de Ouargla, Cité Ennacer, Ouargla, Algérie
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DOI: https://doi.org/10.15372/SJNM20210401
Abstract: In this paper, we study a nonlinear integro-differential Volterra equation with a fractional Caputo derivative. Based on techniques derived from a study of classical Volterra equations, namely Picard's iterative sequence and the product integration method, we propose a complete analytical and numerical study of this equation. Our study is closed by the development of two numerical examples.
Key words: Volterra equation, integro-differential-fractional equation, fixed point, nonlinear equation, product integration method.
Received: 18.07.2019
Revised: 15.01.2021
Accepted: 14.07.2021
English version:
Numerical Analysis and Applications, 2021, Volume 14, Issue 4, Pages 316–334
DOI: https://doi.org/10.1134/S1995423921040029
Bibliographic databases:
Document Type: Article
MSC: 45D05, 45G05, 45J99, 45E99, 65R20
Language: Russian
Citation: S. Guemar, H. Guebbai, S. Lemita, “On an integro-differential fractional nonlinear Volterra-Caputo equation”, Sib. Zh. Vychisl. Mat., 24:4 (2021), 365–382; Num. Anal. Appl., 14:4 (2021), 316–334
Citation in format AMSBIB
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\issue 4
\pages 365--382
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\pages 316--334
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