A boundary value problem with an integral condition for a certain fractional differential equation
The aim of this work is to prove the existence and the uniqueness of the solution of one dimensional initial boundary value problem for a parabolic equation with a Caputo time fractional differential operator supplemented by periodic nonlocal boundary condition and integral condition. First, an a p...
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2025-07-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://journals.vilniustech.lt/index.php/MMA/article/view/21481 |
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| _version_ | 1839639643755118592 |
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| author | Bouthina Sabah Hammou Abdelkader Djerad Ameur Memou Chahla Latrous |
| author_facet | Bouthina Sabah Hammou Abdelkader Djerad Ameur Memou Chahla Latrous |
| author_sort | Bouthina Sabah Hammou |
| collection | DOAJ |
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The aim of this work is to prove the existence and the uniqueness of the solution of one dimensional initial boundary value problem for a parabolic equation with a Caputo time fractional differential operator supplemented by periodic nonlocal boundary condition and integral condition. First, an a priori estimate is established for the associated problem. Secondly, the density of the operator range generated by the considered problem is proved by using the functional analysis method.
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| format | Article |
| id | doaj-art-f7d8dff1e92f45bd8e553a4fb54c3ccf |
| institution | Matheson Library |
| issn | 1392-6292 1648-3510 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj-art-f7d8dff1e92f45bd8e553a4fb54c3ccf2025-07-04T07:50:57ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102025-07-0130310.3846/mma.2025.21481A boundary value problem with an integral condition for a certain fractional differential equationBouthina Sabah Hammou0https://orcid.org/0009-0005-5748-6085Abdelkader Djerad1https://orcid.org/0000-0002-1593-168XAmeur Memou2https://orcid.org/0000-0001-9165-9051Chahla Latrous3https://orcid.org/0009-0002-2367-7404Laboratory of Pure and Applied Mathematics, Department of Mathematics, University of Msila, University Pole, Road Bourdj Bou Arreridj, 28000 Msila, AlgeriaLaboratory of Pure and Applied Mathematics, Department of Mathematics, University of Msila, University Pole, Road Bourdj Bou Arreridj, 28000 Msila, AlgeriaLaboratory of Mathematical Analysis and Application, BBA, Department of Mathematics, University of Msila, 28000 Msila, AlgeriaLaboratory of Differential equations, Departement of Mathematics, Frères Mentouri University, Constantine 1, Algeria The aim of this work is to prove the existence and the uniqueness of the solution of one dimensional initial boundary value problem for a parabolic equation with a Caputo time fractional differential operator supplemented by periodic nonlocal boundary condition and integral condition. First, an a priori estimate is established for the associated problem. Secondly, the density of the operator range generated by the considered problem is proved by using the functional analysis method. https://journals.vilniustech.lt/index.php/MMA/article/view/21481energy inequalityfractional differential equationCaputo derivativesintegral boundary conditionsstrong solution |
| spellingShingle | Bouthina Sabah Hammou Abdelkader Djerad Ameur Memou Chahla Latrous A boundary value problem with an integral condition for a certain fractional differential equation Mathematical Modelling and Analysis energy inequality fractional differential equation Caputo derivatives integral boundary conditions strong solution |
| title | A boundary value problem with an integral condition for a certain fractional differential equation |
| title_full | A boundary value problem with an integral condition for a certain fractional differential equation |
| title_fullStr | A boundary value problem with an integral condition for a certain fractional differential equation |
| title_full_unstemmed | A boundary value problem with an integral condition for a certain fractional differential equation |
| title_short | A boundary value problem with an integral condition for a certain fractional differential equation |
| title_sort | boundary value problem with an integral condition for a certain fractional differential equation |
| topic | energy inequality fractional differential equation Caputo derivatives integral boundary conditions strong solution |
| url | https://journals.vilniustech.lt/index.php/MMA/article/view/21481 |
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