An algorithm for positive solution of boundary value problems of nonlinear fractional differential equations by Adomian decomposition method
In this paper, an algorithm based on a new modification, developed by Duan and Rach, for the Adomian decomposition method (ADM) is generalized to find positive solutions for boundary value problems involving nonlinear fractional ordinary differential equations. In the proposed algorithm the bounda...
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| Format: | Article |
| Language: | English |
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International Scientific Publications and Consulting Services (ISPACS)
2016
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| Online Access: | http://eprints.usm.my/38282/ http://eprints.usm.my/38282/1/An_algorithm_for_positive_solution_of_boundary_value_problems.pdf |
| _version_ | 1848878424891850752 |
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| author | A. I., Md. Ismail Hytham. A., Alkresheh |
| author_facet | A. I., Md. Ismail Hytham. A., Alkresheh |
| author_sort | A. I., Md. Ismail |
| building | USM Institutional Repository |
| collection | Online Access |
| description | In this paper, an algorithm based on a new modification, developed by Duan and Rach, for the Adomian decomposition
method (ADM) is generalized to find positive solutions for boundary value problems involving nonlinear fractional
ordinary differential equations. In the proposed algorithm the boundary conditions are used to convert the nonlinear
fractional differential equations to an equivalent integral equation and then a recursion scheme is used to obtain the
analytical solution components without the use of undetermined coefficients. Hence, there is no requirement to solve
a nonlinear equation or a system of nonlinear equations of undetermined coefficients at each stage of approximation
solution as per in the standard ADM. The fractional derivative is described in the Caputo sense. Numerical examples
are provided to demonstrate the feasibility of the proposed algorithm. |
| first_indexed | 2025-11-15T17:31:07Z |
| format | Article |
| id | usm-38282 |
| institution | Universiti Sains Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T17:31:07Z |
| publishDate | 2016 |
| publisher | International Scientific Publications and Consulting Services (ISPACS) |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | usm-382822018-01-08T07:41:39Z http://eprints.usm.my/38282/ An algorithm for positive solution of boundary value problems of nonlinear fractional differential equations by Adomian decomposition method A. I., Md. Ismail Hytham. A., Alkresheh QA1-939 Mathematics In this paper, an algorithm based on a new modification, developed by Duan and Rach, for the Adomian decomposition method (ADM) is generalized to find positive solutions for boundary value problems involving nonlinear fractional ordinary differential equations. In the proposed algorithm the boundary conditions are used to convert the nonlinear fractional differential equations to an equivalent integral equation and then a recursion scheme is used to obtain the analytical solution components without the use of undetermined coefficients. Hence, there is no requirement to solve a nonlinear equation or a system of nonlinear equations of undetermined coefficients at each stage of approximation solution as per in the standard ADM. The fractional derivative is described in the Caputo sense. Numerical examples are provided to demonstrate the feasibility of the proposed algorithm. International Scientific Publications and Consulting Services (ISPACS) 2016 Article PeerReviewed application/pdf en http://eprints.usm.my/38282/1/An_algorithm_for_positive_solution_of_boundary_value_problems.pdf A. I., Md. Ismail and Hytham. A., Alkresheh (2016) An algorithm for positive solution of boundary value problems of nonlinear fractional differential equations by Adomian decomposition method. Journal of Interpolation and Approximation in Scientific Computing, 2016 (1). pp. 25-37. ISSN 2194-3907 http://www.ispacs.com/journals/jiasc/2016/jiasc-00090/ |
| spellingShingle | QA1-939 Mathematics A. I., Md. Ismail Hytham. A., Alkresheh An algorithm for positive solution of boundary value problems of nonlinear fractional differential equations by Adomian decomposition method |
| title | An algorithm for positive solution of boundary value problems
of nonlinear fractional differential equations by Adomian
decomposition method |
| title_full | An algorithm for positive solution of boundary value problems
of nonlinear fractional differential equations by Adomian
decomposition method |
| title_fullStr | An algorithm for positive solution of boundary value problems
of nonlinear fractional differential equations by Adomian
decomposition method |
| title_full_unstemmed | An algorithm for positive solution of boundary value problems
of nonlinear fractional differential equations by Adomian
decomposition method |
| title_short | An algorithm for positive solution of boundary value problems
of nonlinear fractional differential equations by Adomian
decomposition method |
| title_sort | algorithm for positive solution of boundary value problems
of nonlinear fractional differential equations by adomian
decomposition method |
| topic | QA1-939 Mathematics |
| url | http://eprints.usm.my/38282/ http://eprints.usm.my/38282/ http://eprints.usm.my/38282/1/An_algorithm_for_positive_solution_of_boundary_value_problems.pdf |