Toward the Approximate Solution for Fractional Order Nonlinear Mixed Derivative and Nonlocal Boundary Value Problems
The paper is devoted to the study of operational matrix method for approximating solution for nonlinear coupled system fractional differential equations. The main aim of this paper is to approximate solution for the problem under two different types of boundary conditions, m^-point nonlocal boundary...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/5601821 |
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| _version_ | 1832550311362822144 |
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| author | Hammad Khalil Mohammed Al-Smadi Khaled Moaddy Rahmat Ali Khan Ishak Hashim |
| author_facet | Hammad Khalil Mohammed Al-Smadi Khaled Moaddy Rahmat Ali Khan Ishak Hashim |
| author_sort | Hammad Khalil |
| collection | DOAJ |
| description | The paper is devoted to the study of operational matrix method for approximating solution for nonlinear coupled system fractional differential equations. The main aim of this paper is to approximate solution for the problem under two different types of boundary conditions, m^-point nonlocal boundary conditions and mixed derivative boundary conditions. We develop some new operational matrices. These matrices are used along with some previously derived results to convert the problem under consideration into a system of easily solvable matrix equations. The convergence of the developed scheme is studied analytically and is conformed by solving some test problems. |
| format | Article |
| id | doaj-art-e08fb9fad82c42318c660b6e061d5a6f |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-e08fb9fad82c42318c660b6e061d5a6f2025-02-03T06:07:08ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/56018215601821Toward the Approximate Solution for Fractional Order Nonlinear Mixed Derivative and Nonlocal Boundary Value ProblemsHammad Khalil0Mohammed Al-Smadi1Khaled Moaddy2Rahmat Ali Khan3Ishak Hashim4Department of Mathematics, The University of Poonch Rawalakot, Azad Jammu and Kashmir, PakistanDepartment of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, JordanDepartment of Mathematics, Faculty of Science and Arts, Shaqra University, Shaqra 11691, Saudi ArabiaDepartment of Mathematics, University of Malakand, Chakdara, Lower Dir, Khyber Pakhtunkhwa, PakistanSchool of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, MalaysiaThe paper is devoted to the study of operational matrix method for approximating solution for nonlinear coupled system fractional differential equations. The main aim of this paper is to approximate solution for the problem under two different types of boundary conditions, m^-point nonlocal boundary conditions and mixed derivative boundary conditions. We develop some new operational matrices. These matrices are used along with some previously derived results to convert the problem under consideration into a system of easily solvable matrix equations. The convergence of the developed scheme is studied analytically and is conformed by solving some test problems.http://dx.doi.org/10.1155/2016/5601821 |
| spellingShingle | Hammad Khalil Mohammed Al-Smadi Khaled Moaddy Rahmat Ali Khan Ishak Hashim Toward the Approximate Solution for Fractional Order Nonlinear Mixed Derivative and Nonlocal Boundary Value Problems Discrete Dynamics in Nature and Society |
| title | Toward the Approximate Solution for Fractional Order Nonlinear Mixed Derivative and Nonlocal Boundary Value Problems |
| title_full | Toward the Approximate Solution for Fractional Order Nonlinear Mixed Derivative and Nonlocal Boundary Value Problems |
| title_fullStr | Toward the Approximate Solution for Fractional Order Nonlinear Mixed Derivative and Nonlocal Boundary Value Problems |
| title_full_unstemmed | Toward the Approximate Solution for Fractional Order Nonlinear Mixed Derivative and Nonlocal Boundary Value Problems |
| title_short | Toward the Approximate Solution for Fractional Order Nonlinear Mixed Derivative and Nonlocal Boundary Value Problems |
| title_sort | toward the approximate solution for fractional order nonlinear mixed derivative and nonlocal boundary value problems |
| url | http://dx.doi.org/10.1155/2016/5601821 |
| work_keys_str_mv | AT hammadkhalil towardtheapproximatesolutionforfractionalordernonlinearmixedderivativeandnonlocalboundaryvalueproblems AT mohammedalsmadi towardtheapproximatesolutionforfractionalordernonlinearmixedderivativeandnonlocalboundaryvalueproblems AT khaledmoaddy towardtheapproximatesolutionforfractionalordernonlinearmixedderivativeandnonlocalboundaryvalueproblems AT rahmatalikhan towardtheapproximatesolutionforfractionalordernonlinearmixedderivativeandnonlocalboundaryvalueproblems AT ishakhashim towardtheapproximatesolutionforfractionalordernonlinearmixedderivativeandnonlocalboundaryvalueproblems |