$A numerical algorithm in reproducing kernel-based approach for solving the inverse source problem of the time–space fractional diffusion equation$
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A numerical algorithm in reproducing kernel-based approach for solving the inverse source problem of the time–space fractional diffusion equation

In this analysis, a numerical algorithm in the RKHS approach is utilized to the inverse source problem for the diffusion equation in a time–space fractional sense, where determinations of state variable and source parameter subject to initial–boundary and overdetermination conditions are the main go...

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Autores principales:	Smina Djennadi, Nabil Shawagfeh, Omar Abu Arqub
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Inverse source problem Reproducing kernel Hilbert space Fractional diffusion equation Fractional partial differential equations State variable Source parameter Applied mathematics. Quantitative methods T57-57.97
Acceso en línea:	https://doaj.org/article/69725123a98c40df93ea5d880a827762
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id	oai:doaj.org-article:69725123a98c40df93ea5d880a827762
record_format	dspace
spelling	oai:doaj.org-article:69725123a98c40df93ea5d880a8277622021-11-04T04:43:06ZA numerical algorithm in reproducing kernel-based approach for solving the inverse source problem of the time–space fractional diffusion equation2666-818110.1016/j.padiff.2021.100164https://doaj.org/article/69725123a98c40df93ea5d880a8277622021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2666818121000863https://doaj.org/toc/2666-8181In this analysis, a numerical algorithm in the RKHS approach is utilized to the inverse source problem for the diffusion equation in a time–space fractional sense, where determinations of state variable and source parameter subject to initial–boundary and overdetermination conditions are the main goal. Consequently, specifics theoretical demonstrations are presented to interpret the NPSs to such a fractional problem. In this direction, convergence analysis and error estimates of the developed approach are studied and analyzed as well. Concerning the considered equation, specific unidirectional physical experiments are given in a finite compact regime to confirm the theoretical aspects and to demonstrate the superiority of the utilized approach. Some representative results are presented in two-dimensional graphs, whilst dynamic behaviors of fractional parameters are reported for several fixed α,βvalues. From the practical viewpoint, the archived simulations and consequences justify that the iterative approach is a straightforward and appropriate tool with computational efficiency for numeric solutions of the inverse source problem.Smina DjennadiNabil ShawagfehOmar Abu ArqubElsevierarticleInverse source problemReproducing kernel Hilbert spaceFractional diffusion equationFractional partial differential equationsState variableSource parameterApplied mathematics. Quantitative methodsT57-57.97ENPartial Differential Equations in Applied Mathematics, Vol 4, Iss , Pp 100164- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Inverse source problem Reproducing kernel Hilbert space Fractional diffusion equation Fractional partial differential equations State variable Source parameter Applied mathematics. Quantitative methods T57-57.97
spellingShingle	Inverse source problem Reproducing kernel Hilbert space Fractional diffusion equation Fractional partial differential equations State variable Source parameter Applied mathematics. Quantitative methods T57-57.97 Smina Djennadi Nabil Shawagfeh Omar Abu Arqub A numerical algorithm in reproducing kernel-based approach for solving the inverse source problem of the time–space fractional diffusion equation
description	In this analysis, a numerical algorithm in the RKHS approach is utilized to the inverse source problem for the diffusion equation in a time–space fractional sense, where determinations of state variable and source parameter subject to initial–boundary and overdetermination conditions are the main goal. Consequently, specifics theoretical demonstrations are presented to interpret the NPSs to such a fractional problem. In this direction, convergence analysis and error estimates of the developed approach are studied and analyzed as well. Concerning the considered equation, specific unidirectional physical experiments are given in a finite compact regime to confirm the theoretical aspects and to demonstrate the superiority of the utilized approach. Some representative results are presented in two-dimensional graphs, whilst dynamic behaviors of fractional parameters are reported for several fixed α,βvalues. From the practical viewpoint, the archived simulations and consequences justify that the iterative approach is a straightforward and appropriate tool with computational efficiency for numeric solutions of the inverse source problem.
format	article
author	Smina Djennadi Nabil Shawagfeh Omar Abu Arqub
author_facet	Smina Djennadi Nabil Shawagfeh Omar Abu Arqub
author_sort	Smina Djennadi
title	A numerical algorithm in reproducing kernel-based approach for solving the inverse source problem of the time–space fractional diffusion equation
title_short	A numerical algorithm in reproducing kernel-based approach for solving the inverse source problem of the time–space fractional diffusion equation
title_full	A numerical algorithm in reproducing kernel-based approach for solving the inverse source problem of the time–space fractional diffusion equation
title_fullStr	A numerical algorithm in reproducing kernel-based approach for solving the inverse source problem of the time–space fractional diffusion equation
title_full_unstemmed	A numerical algorithm in reproducing kernel-based approach for solving the inverse source problem of the time–space fractional diffusion equation
title_sort	numerical algorithm in reproducing kernel-based approach for solving the inverse source problem of the time–space fractional diffusion equation
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/69725123a98c40df93ea5d880a827762
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A numerical algorithm in reproducing kernel-based approach for solving the inverse source problem of the time–space fractional diffusion equation

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