Jafari Transformation for Solving a System of Ordinary Differential Equations with Medical Application
| Autor: | Abdullah M. Alsharif, Ahmed I. El-Mesady, Yasser Salah Hamed |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Laplace transform Population Dirac delta function inverse Jafari transform symbols.namesake QA1-939 Applied mathematics education Mathematics QA299.6-433 education.field_of_study Jafari transform Heaviside step function Statistical and Nonlinear Physics Integral transform Algebraic equation Transformation (function) ordinary differential equations Ordinary differential equation symbols Thermodynamics QC310.15-319 Analysis |
| Zdroj: | Fractal and Fractional, Vol 5, Iss 130, p 130 (2021) Fractal and Fractional Volume 5 Issue 3 |
| ISSN: | 2504-3110 |
| DOI: | 10.3390/fractalfract5030130 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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