Solving Linear and Nonlinear Fractional Differential Equations Using Spline Functions
Suitable spline functions of polynomial form are derived and used to solve linear and nonlinear fractional differential equations. The proposed method is applicable for 0<α≤1 and α≥1, where α denotes the order of the fractional derivative in the Caputo sense. The results obtained are in good agre...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/426514 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832548703826608128 |
|---|---|
| author | Adel Al-Rabtah Shaher Momani Mohamed A. Ramadan |
| author_facet | Adel Al-Rabtah Shaher Momani Mohamed A. Ramadan |
| author_sort | Adel Al-Rabtah |
| collection | DOAJ |
| description | Suitable spline functions of polynomial form are derived and used to solve linear and nonlinear
fractional differential equations. The proposed method is applicable for 0<α≤1 and α≥1, where α denotes the order of the fractional derivative in the Caputo sense. The results obtained
are in good agreement with the exact analytical solutions and the numerical results presented
elsewhere. Results also show that the technique introduced here is robust and easy to apply. |
| format | Article |
| id | doaj-art-d0be6b81c4144d9f8a6b4613e14e56ae |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d0be6b81c4144d9f8a6b4613e14e56ae2025-02-03T06:13:22ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/426514426514Solving Linear and Nonlinear Fractional Differential Equations Using Spline FunctionsAdel Al-Rabtah0Shaher Momani1Mohamed A. Ramadan2Department of Mathematics and Statistics, Mutah University, P.O. Box 7, Al-Karak, JordanDepartment of Mathematics and Statistics, University of Jordan, Amman 11942, JordanDepartment of Mathematics, Faculty of Science, Minoufiya University, Shebeen El Koom, Minoufiya, EgyptSuitable spline functions of polynomial form are derived and used to solve linear and nonlinear fractional differential equations. The proposed method is applicable for 0<α≤1 and α≥1, where α denotes the order of the fractional derivative in the Caputo sense. The results obtained are in good agreement with the exact analytical solutions and the numerical results presented elsewhere. Results also show that the technique introduced here is robust and easy to apply.http://dx.doi.org/10.1155/2012/426514 |
| spellingShingle | Adel Al-Rabtah Shaher Momani Mohamed A. Ramadan Solving Linear and Nonlinear Fractional Differential Equations Using Spline Functions Abstract and Applied Analysis |
| title | Solving Linear and Nonlinear Fractional Differential Equations Using Spline Functions |
| title_full | Solving Linear and Nonlinear Fractional Differential Equations Using Spline Functions |
| title_fullStr | Solving Linear and Nonlinear Fractional Differential Equations Using Spline Functions |
| title_full_unstemmed | Solving Linear and Nonlinear Fractional Differential Equations Using Spline Functions |
| title_short | Solving Linear and Nonlinear Fractional Differential Equations Using Spline Functions |
| title_sort | solving linear and nonlinear fractional differential equations using spline functions |
| url | http://dx.doi.org/10.1155/2012/426514 |
| work_keys_str_mv | AT adelalrabtah solvinglinearandnonlinearfractionaldifferentialequationsusingsplinefunctions AT shahermomani solvinglinearandnonlinearfractionaldifferentialequationsusingsplinefunctions AT mohamedaramadan solvinglinearandnonlinearfractionaldifferentialequationsusingsplinefunctions |