Using the Elzaki decomposition method to solve nonlinear fractional differential equations with the Caputo-Fabrizio fractional operator
The techniques of fractional calculus are applied successfully in many branches of science and engineering, one of the techniques is the Elzaki Adomian decomposition method (EADM), which researchers did not study with the fractional derivative of Caputo Fabrizio. This work aims to study the Elzaki...
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| Format: | Article |
| Language: | Arabic |
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College of Science for Women, University of Baghdad
2024-03-01
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| Series: | Baghdad Science Journal |
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| Online Access: | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/7310 |
| _version_ | 1797289087795724288 |
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| author | Mohammed Abdulshareef Hussein |
| author_facet | Mohammed Abdulshareef Hussein |
| author_sort | Mohammed Abdulshareef Hussein |
| collection | DOAJ |
| description |
The techniques of fractional calculus are applied successfully in many branches of science and engineering, one of the techniques is the Elzaki Adomian decomposition method (EADM), which researchers did not study with the fractional derivative of Caputo Fabrizio. This work aims to study the Elzaki Adomian decomposition method (EADM) to solve fractional differential equations with the Caputo-Fabrizio derivative. We presented the algorithm of this method with the CF operator and discussed its convergence by using the method of the Cauchy series then, the method has applied to solve Burger, heat-like, and, couped Burger equations with the Caputo -Fabrizio operator. To conclude the method was convergent and effective for solving this type of fractional differential equations.
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| first_indexed | 2024-03-07T18:59:07Z |
| format | Article |
| id | doaj.art-1b9b99f3cc6b4475aef31fd3c7fad7fc |
| institution | Directory Open Access Journal |
| issn | 2078-8665 2411-7986 |
| language | Arabic |
| last_indexed | 2024-03-07T18:59:07Z |
| publishDate | 2024-03-01 |
| publisher | College of Science for Women, University of Baghdad |
| record_format | Article |
| series | Baghdad Science Journal |
| spelling | doaj.art-1b9b99f3cc6b4475aef31fd3c7fad7fc2024-03-01T20:06:37ZaraCollege of Science for Women, University of BaghdadBaghdad Science Journal2078-86652411-79862024-03-0121310.21123/bsj.2023.7310Using the Elzaki decomposition method to solve nonlinear fractional differential equations with the Caputo-Fabrizio fractional operatorMohammed Abdulshareef Hussein 0Scientific Research Center, AL-Ayen University, Thi-Qar, Iraq The techniques of fractional calculus are applied successfully in many branches of science and engineering, one of the techniques is the Elzaki Adomian decomposition method (EADM), which researchers did not study with the fractional derivative of Caputo Fabrizio. This work aims to study the Elzaki Adomian decomposition method (EADM) to solve fractional differential equations with the Caputo-Fabrizio derivative. We presented the algorithm of this method with the CF operator and discussed its convergence by using the method of the Cauchy series then, the method has applied to solve Burger, heat-like, and, couped Burger equations with the Caputo -Fabrizio operator. To conclude the method was convergent and effective for solving this type of fractional differential equations. https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/7310Burger equation, Caputo-Fabrizio fractional operator, Ezaki decomposition method, Heat-like equation. |
| spellingShingle | Mohammed Abdulshareef Hussein Using the Elzaki decomposition method to solve nonlinear fractional differential equations with the Caputo-Fabrizio fractional operator Baghdad Science Journal Burger equation, Caputo-Fabrizio fractional operator, Ezaki decomposition method, Heat-like equation. |
| title | Using the Elzaki decomposition method to solve nonlinear fractional differential equations with the Caputo-Fabrizio fractional operator |
| title_full | Using the Elzaki decomposition method to solve nonlinear fractional differential equations with the Caputo-Fabrizio fractional operator |
| title_fullStr | Using the Elzaki decomposition method to solve nonlinear fractional differential equations with the Caputo-Fabrizio fractional operator |
| title_full_unstemmed | Using the Elzaki decomposition method to solve nonlinear fractional differential equations with the Caputo-Fabrizio fractional operator |
| title_short | Using the Elzaki decomposition method to solve nonlinear fractional differential equations with the Caputo-Fabrizio fractional operator |
| title_sort | using the elzaki decomposition method to solve nonlinear fractional differential equations with the caputo fabrizio fractional operator |
| topic | Burger equation, Caputo-Fabrizio fractional operator, Ezaki decomposition method, Heat-like equation. |
| url | https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/7310 |
| work_keys_str_mv | AT mohammedabdulshareefhussein usingtheelzakidecompositionmethodtosolvenonlinearfractionaldifferentialequationswiththecaputofabriziofractionaloperator |