A mathematical model and numerical solution for brain tumor derived using fractional operator
In this paper, we present a mathematical model of brain tumor. This model is an extension of a simple two-dimensional mathematical model of glioma growth and diffusion which is derived from fractional operator in terms of Caputo which is called the fractional Burgess equations (FBEs). To obtain a so...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2021-09-01
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| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379721007543 |
| _version_ | 1818733967949430784 |
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| author | R.M. Ganji H. Jafari S.P. Moshokoa N.S. Nkomo |
| author_facet | R.M. Ganji H. Jafari S.P. Moshokoa N.S. Nkomo |
| author_sort | R.M. Ganji |
| collection | DOAJ |
| description | In this paper, we present a mathematical model of brain tumor. This model is an extension of a simple two-dimensional mathematical model of glioma growth and diffusion which is derived from fractional operator in terms of Caputo which is called the fractional Burgess equations (FBEs). To obtain a solution for this model, a numerical technique is presented which is based on operational matrix. First, we assume the solution of the problem under the study is as an expansion of the Bernoulli polynomials. Then with combination of the operational matrix based on the Bernoulli polynomials and collocation method, the problem under the study is changed to a system of nonlinear algebraic equations. Finally, the proposed technique is simulated and tested on three types of the FBEs to confirm the superiority and accuracy. |
| first_indexed | 2024-12-17T23:57:53Z |
| format | Article |
| id | doaj.art-8104ff19526441109d0b87e09be06987 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-12-17T23:57:53Z |
| publishDate | 2021-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-8104ff19526441109d0b87e09be069872022-12-21T21:28:01ZengElsevierResults in Physics2211-37972021-09-0128104671A mathematical model and numerical solution for brain tumor derived using fractional operatorR.M. Ganji0H. Jafari1S.P. Moshokoa2N.S. Nkomo3Department of Applied Mathematics, University of Mazandaran, Babolsar, IranDepartment of Applied Mathematics, University of Mazandaran, Babolsar, Iran; Department of Mathematical Sciences, University of South Africa, UNISA 0003, South Africa; Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 110122, Taiwan; Corresponding author.Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria 0008, South AfricaDepartment of Mathematical Sciences, University of South Africa, UNISA 0003, South AfricaIn this paper, we present a mathematical model of brain tumor. This model is an extension of a simple two-dimensional mathematical model of glioma growth and diffusion which is derived from fractional operator in terms of Caputo which is called the fractional Burgess equations (FBEs). To obtain a solution for this model, a numerical technique is presented which is based on operational matrix. First, we assume the solution of the problem under the study is as an expansion of the Bernoulli polynomials. Then with combination of the operational matrix based on the Bernoulli polynomials and collocation method, the problem under the study is changed to a system of nonlinear algebraic equations. Finally, the proposed technique is simulated and tested on three types of the FBEs to confirm the superiority and accuracy.http://www.sciencedirect.com/science/article/pii/S2211379721007543Brain tumorFractional Burgess equationsBernoulli polynomialsOperational matrixCollocation method |
| spellingShingle | R.M. Ganji H. Jafari S.P. Moshokoa N.S. Nkomo A mathematical model and numerical solution for brain tumor derived using fractional operator Results in Physics Brain tumor Fractional Burgess equations Bernoulli polynomials Operational matrix Collocation method |
| title | A mathematical model and numerical solution for brain tumor derived using fractional operator |
| title_full | A mathematical model and numerical solution for brain tumor derived using fractional operator |
| title_fullStr | A mathematical model and numerical solution for brain tumor derived using fractional operator |
| title_full_unstemmed | A mathematical model and numerical solution for brain tumor derived using fractional operator |
| title_short | A mathematical model and numerical solution for brain tumor derived using fractional operator |
| title_sort | mathematical model and numerical solution for brain tumor derived using fractional operator |
| topic | Brain tumor Fractional Burgess equations Bernoulli polynomials Operational matrix Collocation method |
| url | http://www.sciencedirect.com/science/article/pii/S2211379721007543 |
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