Lebesgue Measurable Function In Fractional Differential Equations
Bassam, M.A. [1], proved some existence and uniqueness theorems for the following fractional linear differential equation.             ..1 With the initial conditions  Where a<x<b, 0< a£1, mk are real numbers, k=1,2,…,n,  pi(x) , F(x) are continuous fu...
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| Format: | Article |
| Language: | English |
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Faculty of Computer Science and Mathematics, University of Kufa
2011-05-01
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| Series: | Journal of Kufa for Mathematics and Computer |
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| Online Access: | https://journal.uokufa.edu.iq/index.php/jkmc/article/view/2146 |
| _version_ | 1797266969862340608 |
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| author | Sabah Mahmood Shaker |
| author_facet | Sabah Mahmood Shaker |
| author_sort | Sabah Mahmood Shaker |
| collection | DOAJ |
| description |
Bassam, M.A. [1], proved some existence and uniqueness theorems for the following fractional linear differential equation.
            ..1
With the initial conditions
Â
Where a<x<b, 0< a£1, mk are real numbers, k=1,2,…,n,  pi(x) , F(x) are continuous functions defined on (a,b) such that p0(x)≠0, i=0,1…,n and y[(n-i) α] denotes the fractional derivative of order (n-i)α for the function y.
In this work we prove some theorems for equation (1), however for α=1. Equation (1) is an ordinary differential equation of order n, therefore all the theorems proved here will be reduced to well known result in the theory of ordinary differential equations. Moreover,
We give some examples and an application for equation (1).
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| first_indexed | 2024-04-25T01:09:08Z |
| format | Article |
| id | doaj.art-3c09e7ac36cd4156b89b9043b3c56053 |
| institution | Directory Open Access Journal |
| issn | 2076-1171 2518-0010 |
| language | English |
| last_indexed | 2024-04-25T01:09:08Z |
| publishDate | 2011-05-01 |
| publisher | Faculty of Computer Science and Mathematics, University of Kufa |
| record_format | Article |
| series | Journal of Kufa for Mathematics and Computer |
| spelling | doaj.art-3c09e7ac36cd4156b89b9043b3c560532024-03-10T10:59:06ZengFaculty of Computer Science and Mathematics, University of KufaJournal of Kufa for Mathematics and Computer2076-11712518-00102011-05-011310.31642/JoKMC/2018/010303Lebesgue Measurable Function In Fractional Differential EquationsSabah Mahmood Shaker0Al_Mustansiriya University Bassam, M.A. [1], proved some existence and uniqueness theorems for the following fractional linear differential equation.             ..1 With the initial conditions  Where a<x<b, 0< a£1, mk are real numbers, k=1,2,…,n,  pi(x) , F(x) are continuous functions defined on (a,b) such that p0(x)≠0, i=0,1…,n and y[(n-i) α] denotes the fractional derivative of order (n-i)α for the function y. In this work we prove some theorems for equation (1), however for α=1. Equation (1) is an ordinary differential equation of order n, therefore all the theorems proved here will be reduced to well known result in the theory of ordinary differential equations. Moreover, We give some examples and an application for equation (1). https://journal.uokufa.edu.iq/index.php/jkmc/article/view/2146Ordinary Differential Equations Lebesgue Measurable Function Fractional Differential Equations. |
| spellingShingle | Sabah Mahmood Shaker Lebesgue Measurable Function In Fractional Differential Equations Journal of Kufa for Mathematics and Computer Ordinary Differential Equations Lebesgue Measurable Function Fractional Differential Equations. |
| title | Lebesgue Measurable Function In Fractional Differential Equations |
| title_full | Lebesgue Measurable Function In Fractional Differential Equations |
| title_fullStr | Lebesgue Measurable Function In Fractional Differential Equations |
| title_full_unstemmed | Lebesgue Measurable Function In Fractional Differential Equations |
| title_short | Lebesgue Measurable Function In Fractional Differential Equations |
| title_sort | lebesgue measurable function in fractional differential equations |
| topic | Ordinary Differential Equations Lebesgue Measurable Function Fractional Differential Equations. |
| url | https://journal.uokufa.edu.iq/index.php/jkmc/article/view/2146 |
| work_keys_str_mv | AT sabahmahmoodshaker lebesguemeasurablefunctioninfractionaldifferentialequations |