Construction of fractional power series solutions to fractional stiff system using residual functions algorithm
Abstract A powerful analytical approach, namely the fractional residual power series method (FRPS), is applied successfully in this work to solving a class of fractional stiff systems. The methodology of the FRPS method gets a Maclaurin expansion of the solution in rapidly convergent form and appare...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-03-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-019-2042-3 |
| _version_ | 1818503215898951680 |
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| author | Asad Freihet Shatha Hasan Mohammed Al-Smadi Mohamed Gaith Shaher Momani |
| author_facet | Asad Freihet Shatha Hasan Mohammed Al-Smadi Mohamed Gaith Shaher Momani |
| author_sort | Asad Freihet |
| collection | DOAJ |
| description | Abstract A powerful analytical approach, namely the fractional residual power series method (FRPS), is applied successfully in this work to solving a class of fractional stiff systems. The methodology of the FRPS method gets a Maclaurin expansion of the solution in rapidly convergent form and apparent sequences based on the Caputo sense without any restriction hypothesis. This approach is tested on a fractional stiff system with nonlinearity ranging. Meanwhile, stability and convergence study are presented in the domain of interest. Illustrative examples justify that the proposed method is analytically effective and convenient, and it can be implemented in a large number of engineering problems. A numerical comparison for the experimental data with another well-known method, the reproducing kernel method, is given. The graphical consequences illuminate the simplicity and reliability of the FRPS method in the determination of the RPS solutions consistently. |
| first_indexed | 2024-12-10T21:21:05Z |
| format | Article |
| id | doaj.art-38d3774b126941e38159071102e67c31 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-10T21:21:05Z |
| publishDate | 2019-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-38d3774b126941e38159071102e67c312022-12-22T01:33:08ZengSpringerOpenAdvances in Difference Equations1687-18472019-03-012019111510.1186/s13662-019-2042-3Construction of fractional power series solutions to fractional stiff system using residual functions algorithmAsad Freihet0Shatha Hasan1Mohammed Al-Smadi2Mohamed Gaith3Shaher Momani4Department of Applied Science, Ajloun College, Al-Balqa Applied UniversityDepartment of Applied Science, Ajloun College, Al-Balqa Applied UniversityDepartment of Applied Science, Ajloun College, Al-Balqa Applied UniversityFaculty of Engineering Technology, Al-Balqa Applied UniversityDepartment of Mathematics, Faculty of Science, The University of JordanAbstract A powerful analytical approach, namely the fractional residual power series method (FRPS), is applied successfully in this work to solving a class of fractional stiff systems. The methodology of the FRPS method gets a Maclaurin expansion of the solution in rapidly convergent form and apparent sequences based on the Caputo sense without any restriction hypothesis. This approach is tested on a fractional stiff system with nonlinearity ranging. Meanwhile, stability and convergence study are presented in the domain of interest. Illustrative examples justify that the proposed method is analytically effective and convenient, and it can be implemented in a large number of engineering problems. A numerical comparison for the experimental data with another well-known method, the reproducing kernel method, is given. The graphical consequences illuminate the simplicity and reliability of the FRPS method in the determination of the RPS solutions consistently.http://link.springer.com/article/10.1186/s13662-019-2042-3Residual power series methodFractional stiff systemCaputo derivativeResidual errorGeneralized Taylor series |
| spellingShingle | Asad Freihet Shatha Hasan Mohammed Al-Smadi Mohamed Gaith Shaher Momani Construction of fractional power series solutions to fractional stiff system using residual functions algorithm Advances in Difference Equations Residual power series method Fractional stiff system Caputo derivative Residual error Generalized Taylor series |
| title | Construction of fractional power series solutions to fractional stiff system using residual functions algorithm |
| title_full | Construction of fractional power series solutions to fractional stiff system using residual functions algorithm |
| title_fullStr | Construction of fractional power series solutions to fractional stiff system using residual functions algorithm |
| title_full_unstemmed | Construction of fractional power series solutions to fractional stiff system using residual functions algorithm |
| title_short | Construction of fractional power series solutions to fractional stiff system using residual functions algorithm |
| title_sort | construction of fractional power series solutions to fractional stiff system using residual functions algorithm |
| topic | Residual power series method Fractional stiff system Caputo derivative Residual error Generalized Taylor series |
| url | http://link.springer.com/article/10.1186/s13662-019-2042-3 |
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