Jafari Transformation for Solving a System of Ordinary Differential Equations with Medical Application
Integral transformations are essential for solving complex problems in business, engineering, natural sciences, computers, optical science, and modern mathematics. In this paper, we apply a general integral transform, called the Jafari transform, for solving a system of ordinary differential equatio...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-09-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/5/3/130 |
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| author | Ahmed I. El-Mesady Yasser S. Hamed Abdullah M. Alsharif |
| author_facet | Ahmed I. El-Mesady Yasser S. Hamed Abdullah M. Alsharif |
| author_sort | Ahmed I. El-Mesady |
| collection | DOAJ |
| description | Integral transformations are essential for solving complex problems in business, engineering, natural sciences, computers, optical science, and modern mathematics. In this paper, we apply a general integral transform, called the Jafari transform, for solving a system of ordinary differential equations. After applying the Jafari transform, ordinary differential equations are converted to a simple system of algebraic equations that can be solved easily. Then, by using the inverse operator of the Jafari transform, we can solve the main system of ordinary differential equations. Jafari transform belongs to the class of Laplace transform and is considered a generalization to integral transforms such as Laplace, Elzaki, Sumudu, G\_transforms, Aboodh, Pourreza, etc. Jafari transform does not need a large computational work as the previous integral transforms. For the Jafari transform, we have studied some valuable properties and theories that have not been studied before. Such as the linearity property, scaling property, first and second shift properties, the transformation of periodic functions, Heaviside function, and the transformation of Dirac’s delta function, and so on. There is a mathematical model that describes the cell population dynamics in the colonic crypt and colorectal cancer. We have applied the Jafari transform for solving this model. |
| first_indexed | 2024-03-10T07:39:49Z |
| format | Article |
| id | doaj.art-963aa3abca1144ef853af9c9606cde30 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T07:39:49Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-963aa3abca1144ef853af9c9606cde302023-11-22T13:10:03ZengMDPI AGFractal and Fractional2504-31102021-09-015313010.3390/fractalfract5030130Jafari Transformation for Solving a System of Ordinary Differential Equations with Medical ApplicationAhmed I. El-Mesady0Yasser S. Hamed1Abdullah M. Alsharif2Department of Physics and Engineering Mathematics, Faculty of Electronic Engineering, Menoufia University, Menouf 32952, EgyptDepartment of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaDepartment of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaIntegral transformations are essential for solving complex problems in business, engineering, natural sciences, computers, optical science, and modern mathematics. In this paper, we apply a general integral transform, called the Jafari transform, for solving a system of ordinary differential equations. After applying the Jafari transform, ordinary differential equations are converted to a simple system of algebraic equations that can be solved easily. Then, by using the inverse operator of the Jafari transform, we can solve the main system of ordinary differential equations. Jafari transform belongs to the class of Laplace transform and is considered a generalization to integral transforms such as Laplace, Elzaki, Sumudu, G\_transforms, Aboodh, Pourreza, etc. Jafari transform does not need a large computational work as the previous integral transforms. For the Jafari transform, we have studied some valuable properties and theories that have not been studied before. Such as the linearity property, scaling property, first and second shift properties, the transformation of periodic functions, Heaviside function, and the transformation of Dirac’s delta function, and so on. There is a mathematical model that describes the cell population dynamics in the colonic crypt and colorectal cancer. We have applied the Jafari transform for solving this model.https://www.mdpi.com/2504-3110/5/3/130Laplace transformJafari transforminverse Jafari transformordinary differential equations |
| spellingShingle | Ahmed I. El-Mesady Yasser S. Hamed Abdullah M. Alsharif Jafari Transformation for Solving a System of Ordinary Differential Equations with Medical Application Fractal and Fractional Laplace transform Jafari transform inverse Jafari transform ordinary differential equations |
| title | Jafari Transformation for Solving a System of Ordinary Differential Equations with Medical Application |
| title_full | Jafari Transformation for Solving a System of Ordinary Differential Equations with Medical Application |
| title_fullStr | Jafari Transformation for Solving a System of Ordinary Differential Equations with Medical Application |
| title_full_unstemmed | Jafari Transformation for Solving a System of Ordinary Differential Equations with Medical Application |
| title_short | Jafari Transformation for Solving a System of Ordinary Differential Equations with Medical Application |
| title_sort | jafari transformation for solving a system of ordinary differential equations with medical application |
| topic | Laplace transform Jafari transform inverse Jafari transform ordinary differential equations |
| url | https://www.mdpi.com/2504-3110/5/3/130 |
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