$Effective numerical technique for nonlinear Caputo-Fabrizio systems of fractional Volterra integro-differential equations in Hilbert space$
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Effective numerical technique for nonlinear Caputo-Fabrizio systems of fractional Volterra integro-differential equations in Hilbert space

The point of this paper is to analyze and investigate the analytic-approximate solutions for fractional system of Volterra integro-differential equations in framework of Caputo-Fabrizio operator. The methodology relies on creating the reproducing kernel functions to gain analytical solutions in a un...

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Autores principales:	Fatima Youbi, Shaher Momani, Shatha Hasan, Mohammed Al-Smadi
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2022
Materias:	Iterative reproducing kernel algorithm Caputo-Fabrizio operator Fractional integro-differntial equations Stability analysis Numerical solution Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/21e642080b7b436ba04c0472ff648b47
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id	oai:doaj.org-article:21e642080b7b436ba04c0472ff648b47
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spelling	oai:doaj.org-article:21e642080b7b436ba04c0472ff648b472021-11-30T04:13:44ZEffective numerical technique for nonlinear Caputo-Fabrizio systems of fractional Volterra integro-differential equations in Hilbert space1110-016810.1016/j.aej.2021.06.086https://doaj.org/article/21e642080b7b436ba04c0472ff648b472022-03-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S1110016821004488https://doaj.org/toc/1110-0168The point of this paper is to analyze and investigate the analytic-approximate solutions for fractional system of Volterra integro-differential equations in framework of Caputo-Fabrizio operator. The methodology relies on creating the reproducing kernel functions to gain analytical solutions in a uniform form of a rapidly convergent series in the Hilbert space. Using the Gram-Schmidt orthonomalization process, the orthonormal basis system is constructed in a dense compact domain to encompass the Fourier series expansion in view of reproducing kernel properties. Besides, convergence and error analysis of the proposed technique are discussed. For this purpose, several numerical examples are tested to demonstrate the great feasibility and efficiency of the present method and to support theoretical aspect as well. From a numerical point of view, the acquired solutions simulation indicates that the methodology used is sound, straightforward, and appropriate to deal with many physical issues in light of Caputo-Fabrizio derivatives.Fatima YoubiShaher MomaniShatha HasanMohammed Al-SmadiElsevierarticleIterative reproducing kernel algorithmCaputo-Fabrizio operatorFractional integro-differntial equationsStability analysisNumerical solutionEngineering (General). Civil engineering (General)TA1-2040ENAlexandria Engineering Journal, Vol 61, Iss 3, Pp 1778-1786 (2022)
institution	DOAJ
collection	DOAJ
language	EN
topic	Iterative reproducing kernel algorithm Caputo-Fabrizio operator Fractional integro-differntial equations Stability analysis Numerical solution Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	Iterative reproducing kernel algorithm Caputo-Fabrizio operator Fractional integro-differntial equations Stability analysis Numerical solution Engineering (General). Civil engineering (General) TA1-2040 Fatima Youbi Shaher Momani Shatha Hasan Mohammed Al-Smadi Effective numerical technique for nonlinear Caputo-Fabrizio systems of fractional Volterra integro-differential equations in Hilbert space
description	The point of this paper is to analyze and investigate the analytic-approximate solutions for fractional system of Volterra integro-differential equations in framework of Caputo-Fabrizio operator. The methodology relies on creating the reproducing kernel functions to gain analytical solutions in a uniform form of a rapidly convergent series in the Hilbert space. Using the Gram-Schmidt orthonomalization process, the orthonormal basis system is constructed in a dense compact domain to encompass the Fourier series expansion in view of reproducing kernel properties. Besides, convergence and error analysis of the proposed technique are discussed. For this purpose, several numerical examples are tested to demonstrate the great feasibility and efficiency of the present method and to support theoretical aspect as well. From a numerical point of view, the acquired solutions simulation indicates that the methodology used is sound, straightforward, and appropriate to deal with many physical issues in light of Caputo-Fabrizio derivatives.
format	article
author	Fatima Youbi Shaher Momani Shatha Hasan Mohammed Al-Smadi
author_facet	Fatima Youbi Shaher Momani Shatha Hasan Mohammed Al-Smadi
author_sort	Fatima Youbi
title	Effective numerical technique for nonlinear Caputo-Fabrizio systems of fractional Volterra integro-differential equations in Hilbert space
title_short	Effective numerical technique for nonlinear Caputo-Fabrizio systems of fractional Volterra integro-differential equations in Hilbert space
title_full	Effective numerical technique for nonlinear Caputo-Fabrizio systems of fractional Volterra integro-differential equations in Hilbert space
title_fullStr	Effective numerical technique for nonlinear Caputo-Fabrizio systems of fractional Volterra integro-differential equations in Hilbert space
title_full_unstemmed	Effective numerical technique for nonlinear Caputo-Fabrizio systems of fractional Volterra integro-differential equations in Hilbert space
title_sort	effective numerical technique for nonlinear caputo-fabrizio systems of fractional volterra integro-differential equations in hilbert space
publisher	Elsevier
publishDate	2022
url	https://doaj.org/article/21e642080b7b436ba04c0472ff648b47
work_keys_str_mv	AT fatimayoubi effectivenumericaltechniquefornonlinearcaputofabriziosystemsoffractionalvolterraintegrodifferentialequationsinhilbertspace AT shahermomani effectivenumericaltechniquefornonlinearcaputofabriziosystemsoffractionalvolterraintegrodifferentialequationsinhilbertspace AT shathahasan effectivenumericaltechniquefornonlinearcaputofabriziosystemsoffractionalvolterraintegrodifferentialequationsinhilbertspace AT mohammedalsmadi effectivenumericaltechniquefornonlinearcaputofabriziosystemsoffractionalvolterraintegrodifferentialequationsinhilbertspace
_version_	1718406850404155392

Effective numerical technique for nonlinear Caputo-Fabrizio systems of fractional Volterra integro-differential equations in Hilbert space

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