A Bi-Geometric Fractional Model for the Treatment of Cancer Using Radiotherapy
Our study is based on the modification of a well-known predator-prey equation, or the Lotka–Volterra competition model. That is, a system of differential equations was established for the population of healthy and cancerous cells within the tumor tissue of a patient struggling with cancer. Besides,...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/6/6/287 |
| _version_ | 1797487340651806720 |
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| author | Mohammad Momenzadeh Olivia Ada Obi Evren Hincal |
| author_facet | Mohammad Momenzadeh Olivia Ada Obi Evren Hincal |
| author_sort | Mohammad Momenzadeh |
| collection | DOAJ |
| description | Our study is based on the modification of a well-known predator-prey equation, or the Lotka–Volterra competition model. That is, a system of differential equations was established for the population of healthy and cancerous cells within the tumor tissue of a patient struggling with cancer. Besides, fractional differentiation remedies the situation by obtaining a meticulous model with more flexible parameters. Furthermore, a specific type of non-Newtonian calculus, bi-geometric calculus, can describe the model in terms of proportions and implies the alternative aspect of a dynamic system. Moreover, fractional operators in bi-geometric calculus are formulated in terms of Hadamard fractional operators. In this article, the development of fractional operators in non-Newtonian calculus was investigated. The model was extended in these criteria, and the existence and uniqueness of the model were considered and guaranteed in the first step by applying the Arzelà–Ascoli. The bi-geometric analogue of the numerical method provided a suitable tool to solve the model approximately. In the end, the visual graphs were obtained by using the MATLAB program. |
| first_indexed | 2024-03-09T23:47:14Z |
| format | Article |
| id | doaj.art-e45abfa6ff7844dea6be4bcd6b4e8664 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T23:47:14Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-e45abfa6ff7844dea6be4bcd6b4e86642023-11-23T16:42:11ZengMDPI AGFractal and Fractional2504-31102022-05-016628710.3390/fractalfract6060287A Bi-Geometric Fractional Model for the Treatment of Cancer Using RadiotherapyMohammad Momenzadeh0Olivia Ada Obi1Evren Hincal2Department of Mathematics, Near East University, Nicosia 99138, CyprusDepartment of Mathematics, Near East University, Nicosia 99138, CyprusDepartment of Mathematics, Near East University, Nicosia 99138, CyprusOur study is based on the modification of a well-known predator-prey equation, or the Lotka–Volterra competition model. That is, a system of differential equations was established for the population of healthy and cancerous cells within the tumor tissue of a patient struggling with cancer. Besides, fractional differentiation remedies the situation by obtaining a meticulous model with more flexible parameters. Furthermore, a specific type of non-Newtonian calculus, bi-geometric calculus, can describe the model in terms of proportions and implies the alternative aspect of a dynamic system. Moreover, fractional operators in bi-geometric calculus are formulated in terms of Hadamard fractional operators. In this article, the development of fractional operators in non-Newtonian calculus was investigated. The model was extended in these criteria, and the existence and uniqueness of the model were considered and guaranteed in the first step by applying the Arzelà–Ascoli. The bi-geometric analogue of the numerical method provided a suitable tool to solve the model approximately. In the end, the visual graphs were obtained by using the MATLAB program.https://www.mdpi.com/2504-3110/6/6/287Lotka–Volterra competition modelbi-geometric calculusHadamard operatorfractional operator |
| spellingShingle | Mohammad Momenzadeh Olivia Ada Obi Evren Hincal A Bi-Geometric Fractional Model for the Treatment of Cancer Using Radiotherapy Fractal and Fractional Lotka–Volterra competition model bi-geometric calculus Hadamard operator fractional operator |
| title | A Bi-Geometric Fractional Model for the Treatment of Cancer Using Radiotherapy |
| title_full | A Bi-Geometric Fractional Model for the Treatment of Cancer Using Radiotherapy |
| title_fullStr | A Bi-Geometric Fractional Model for the Treatment of Cancer Using Radiotherapy |
| title_full_unstemmed | A Bi-Geometric Fractional Model for the Treatment of Cancer Using Radiotherapy |
| title_short | A Bi-Geometric Fractional Model for the Treatment of Cancer Using Radiotherapy |
| title_sort | bi geometric fractional model for the treatment of cancer using radiotherapy |
| topic | Lotka–Volterra competition model bi-geometric calculus Hadamard operator fractional operator |
| url | https://www.mdpi.com/2504-3110/6/6/287 |
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