Well-posedness of the inverse problem of time fractional heat equation in the sense of the Atangana-Baleanu fractional approach

Well-posedness of the inverse problem of time fractional heat equation in the sense of the Atangana-Baleanu fractional approach

In the present work, an inverse problem for the heat equation in two dimensional space with Robin boundary condition that involving a new fractional derivative, namely, Atangana-Baleanu approach with non-local and non-singular kernel is considered. An explicit solution set {u(x,y,t),a(t)} of the giv...

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Main Authors: Smina Djennadi, Nabil Shawagfeh, Omar Abu Arqub
Format: Article
Language:English
Published: Elsevier 2020-08-01
Series:Alexandria Engineering Journal
Subjects:
Inverse problem
Atangana-Baleanu derivative
Robin boundary conditions
Eigenfunctions expansion method
Volterra integral equation
Online Access:http://www.sciencedirect.com/science/article/pii/S111001682030065X
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spelling doaj-9e3f0f1fa8634a84bde1c280d8c787222021-06-02T13:31:34ZengElsevierAlexandria Engineering Journal1110-01682020-08-0159422612268Well-posedness of the inverse problem of time fractional heat equation in the sense of the Atangana-Baleanu fractional approachSmina Djennadi0Nabil Shawagfeh1Omar Abu Arqub2Department of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, JordanDepartment of Mathematics, Faculty of Science, The University of Jordan, Amman 11942, JordanDepartment of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, Jordan; Corresponding author.In the present work, an inverse problem for the heat equation in two dimensional space with Robin boundary condition that involving a new fractional derivative, namely, Atangana-Baleanu approach with non-local and non-singular kernel is considered. An explicit solution set {u(x,y,t),a(t)} of the given inverse problem is obtained by using the eigenfunctions expansion method and the integral overdetermination condition. Under some assumptions the existence, uniqueness of the suggested solution, and its continuous dependence on the data are proved.http://www.sciencedirect.com/science/article/pii/S111001682030065XInverse problemAtangana-Baleanu derivativeRobin boundary conditionsEigenfunctions expansion methodVolterra integral equation
collection DOAJ
language English
format Article
sources DOAJ
author Smina Djennadi
Nabil Shawagfeh
Omar Abu Arqub
spellingShingle Smina Djennadi
Nabil Shawagfeh
Omar Abu Arqub
Well-posedness of the inverse problem of time fractional heat equation in the sense of the Atangana-Baleanu fractional approach
Alexandria Engineering Journal
Inverse problem
Atangana-Baleanu derivative
Robin boundary conditions
Eigenfunctions expansion method
Volterra integral equation
author_facet Smina Djennadi
Nabil Shawagfeh
Omar Abu Arqub
author_sort Smina Djennadi
title Well-posedness of the inverse problem of time fractional heat equation in the sense of the Atangana-Baleanu fractional approach
title_short Well-posedness of the inverse problem of time fractional heat equation in the sense of the Atangana-Baleanu fractional approach
title_full Well-posedness of the inverse problem of time fractional heat equation in the sense of the Atangana-Baleanu fractional approach
title_fullStr Well-posedness of the inverse problem of time fractional heat equation in the sense of the Atangana-Baleanu fractional approach
title_full_unstemmed Well-posedness of the inverse problem of time fractional heat equation in the sense of the Atangana-Baleanu fractional approach
title_sort well-posedness of the inverse problem of time fractional heat equation in the sense of the atangana-baleanu fractional approach
publisher Elsevier
series Alexandria Engineering Journal
issn 1110-0168
publishDate 2020-08-01
description In the present work, an inverse problem for the heat equation in two dimensional space with Robin boundary condition that involving a new fractional derivative, namely, Atangana-Baleanu approach with non-local and non-singular kernel is considered. An explicit solution set {u(x,y,t),a(t)} of the given inverse problem is obtained by using the eigenfunctions expansion method and the integral overdetermination condition. Under some assumptions the existence, uniqueness of the suggested solution, and its continuous dependence on the data are proved.
topic Inverse problem
Atangana-Baleanu derivative
Robin boundary conditions
Eigenfunctions expansion method
Volterra integral equation
url http://www.sciencedirect.com/science/article/pii/S111001682030065X
work_keys_str_mv AT sminadjennadi wellposednessoftheinverseproblemoftimefractionalheatequationinthesenseoftheatanganabaleanufractionalapproach
AT nabilshawagfeh wellposednessoftheinverseproblemoftimefractionalheatequationinthesenseoftheatanganabaleanufractionalapproach
AT omarabuarqub wellposednessoftheinverseproblemoftimefractionalheatequationinthesenseoftheatanganabaleanufractionalapproach
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