Laplace decomposition for solving nonlinear system of fractional order partial differential equations
Abstract In the present article a modified decomposition method is implemented to solve systems of partial differential equations of fractional-order derivatives. The derivatives of fractional-order are expressed in terms of Caputo operator. The validity of the proposed method is analyzed through il...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-07-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02839-y |
| _version_ | 1819159829644574720 |
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| author | Hassan Khan Rasool Shah Poom Kumam Dumitru Baleanu Muhammad Arif |
| author_facet | Hassan Khan Rasool Shah Poom Kumam Dumitru Baleanu Muhammad Arif |
| author_sort | Hassan Khan |
| collection | DOAJ |
| description | Abstract In the present article a modified decomposition method is implemented to solve systems of partial differential equations of fractional-order derivatives. The derivatives of fractional-order are expressed in terms of Caputo operator. The validity of the proposed method is analyzed through illustrative examples. The solution graphs have shown a close contact between the exact and LADM solutions. It is observed that the solutions of fractional-order problems converge towards the solution of an integer-order problem, which confirmed the reliability of the suggested technique. Due to better accuracy and straightforward implementation, the extension of the present method can be made to solve other fractional-order problems. |
| first_indexed | 2024-12-22T16:46:46Z |
| format | Article |
| id | doaj.art-22f71d5cbb3d48be9c29240c78d9d2a8 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-22T16:46:46Z |
| publishDate | 2020-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-22f71d5cbb3d48be9c29240c78d9d2a82022-12-21T18:19:43ZengSpringerOpenAdvances in Difference Equations1687-18472020-07-012020111810.1186/s13662-020-02839-yLaplace decomposition for solving nonlinear system of fractional order partial differential equationsHassan Khan0Rasool Shah1Poom Kumam2Dumitru Baleanu3Muhammad Arif4Department of Mathematics, Abdul Wali khan UniversityDepartment of Mathematics, Abdul Wali khan UniversityTheoretical and Computational Science (TaCS) Center Department of Mathematics, Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT)Department of Mathematics, Faculty of Arts and Sciences, Cankaya UniversityDepartment of Mathematics, Abdul Wali khan UniversityAbstract In the present article a modified decomposition method is implemented to solve systems of partial differential equations of fractional-order derivatives. The derivatives of fractional-order are expressed in terms of Caputo operator. The validity of the proposed method is analyzed through illustrative examples. The solution graphs have shown a close contact between the exact and LADM solutions. It is observed that the solutions of fractional-order problems converge towards the solution of an integer-order problem, which confirmed the reliability of the suggested technique. Due to better accuracy and straightforward implementation, the extension of the present method can be made to solve other fractional-order problems.http://link.springer.com/article/10.1186/s13662-020-02839-yCaputo operatorAdomian decomposition methodLaplace transformationFractional systems of partial differential equations |
| spellingShingle | Hassan Khan Rasool Shah Poom Kumam Dumitru Baleanu Muhammad Arif Laplace decomposition for solving nonlinear system of fractional order partial differential equations Advances in Difference Equations Caputo operator Adomian decomposition method Laplace transformation Fractional systems of partial differential equations |
| title | Laplace decomposition for solving nonlinear system of fractional order partial differential equations |
| title_full | Laplace decomposition for solving nonlinear system of fractional order partial differential equations |
| title_fullStr | Laplace decomposition for solving nonlinear system of fractional order partial differential equations |
| title_full_unstemmed | Laplace decomposition for solving nonlinear system of fractional order partial differential equations |
| title_short | Laplace decomposition for solving nonlinear system of fractional order partial differential equations |
| title_sort | laplace decomposition for solving nonlinear system of fractional order partial differential equations |
| topic | Caputo operator Adomian decomposition method Laplace transformation Fractional systems of partial differential equations |
| url | http://link.springer.com/article/10.1186/s13662-020-02839-y |
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