Determination of the Order of Fractional Derivative for Subdiffusion Equations

The identification of the right order of the equation in applied fractional modeling plays an important role. In this paper we consider an inverse problem for determining the order of time fractional derivative in a subdiffusion equation with an arbitrary second order elliptic differential operator....

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Detalles Bibliográficos
Autores principales: Ashurov, Ravshan, Umarov, Sabir
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Versita 2020
Materias:
Research Paper
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8617357/
https://www.ncbi.nlm.nih.gov/pubmed/34849078
http://dx.doi.org/10.1515/fca-2020-0081
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author Ashurov, Ravshan
Umarov, Sabir
author_facet Ashurov, Ravshan
Umarov, Sabir
author_sort Ashurov, Ravshan
collection PubMed
description The identification of the right order of the equation in applied fractional modeling plays an important role. In this paper we consider an inverse problem for determining the order of time fractional derivative in a subdiffusion equation with an arbitrary second order elliptic differential operator. We prove that the additional information about the solution at a fixed time instant at a monitoring location, as “the observation data”, identifies uniquely the order of the fractional derivative.
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spelling pubmed-86173572021-11-26 Determination of the Order of Fractional Derivative for Subdiffusion Equations Ashurov, Ravshan Umarov, Sabir Fract Calc Appl Anal Research Paper The identification of the right order of the equation in applied fractional modeling plays an important role. In this paper we consider an inverse problem for determining the order of time fractional derivative in a subdiffusion equation with an arbitrary second order elliptic differential operator. We prove that the additional information about the solution at a fixed time instant at a monitoring location, as “the observation data”, identifies uniquely the order of the fractional derivative. Versita 2020-12-31 2020 /pmc/articles/PMC8617357/ /pubmed/34849078 http://dx.doi.org/10.1515/fca-2020-0081 Text en © Diogenes Co., Sofia 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Research Paper
Ashurov, Ravshan
Umarov, Sabir
Determination of the Order of Fractional Derivative for Subdiffusion Equations
title Determination of the Order of Fractional Derivative for Subdiffusion Equations
title_full Determination of the Order of Fractional Derivative for Subdiffusion Equations
title_fullStr Determination of the Order of Fractional Derivative for Subdiffusion Equations
title_full_unstemmed Determination of the Order of Fractional Derivative for Subdiffusion Equations
title_short Determination of the Order of Fractional Derivative for Subdiffusion Equations
title_sort determination of the order of fractional derivative for subdiffusion equations
topic Research Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8617357/
https://www.ncbi.nlm.nih.gov/pubmed/34849078
http://dx.doi.org/10.1515/fca-2020-0081
work_keys_str_mv AT ashurovravshan determinationoftheorderoffractionalderivativeforsubdiffusionequations
AT umarovsabir determinationoftheorderoffractionalderivativeforsubdiffusionequations

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