Two efficient methods for solving fractional Lane–Emden equations with conformable fractional derivative
Abstract In this paper, we introduce two reliable efficient approximate methods for solving a class of fractional Lane–Emden equations with conformable fractional derivative (CL-M) which are the so-called conformable Homotopy–Adomian decomposition method (CH-A) and conformable residual power series...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-08-01
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| Series: | Journal of the Egyptian Mathematical Society |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s42787-020-00099-z |
| _version_ | 1818964716952748032 |
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| author | Adyan M. Malik Osama H. Mohammed |
| author_facet | Adyan M. Malik Osama H. Mohammed |
| author_sort | Adyan M. Malik |
| collection | DOAJ |
| description | Abstract In this paper, we introduce two reliable efficient approximate methods for solving a class of fractional Lane–Emden equations with conformable fractional derivative (CL-M) which are the so-called conformable Homotopy–Adomian decomposition method (CH-A) and conformable residual power series method (CRP). Furthermore, the proposed methods express the solutions of the non-linear cases of the CL-M in terms of fractional convergent series in which its components can be computed in an easy manner. Finally, the results are given by graphs for each case of the CL-M at different values of α in order to demonstrate its accuracy, applicability, and efficiency. |
| first_indexed | 2024-12-20T13:05:32Z |
| format | Article |
| id | doaj.art-e1395525a0fe405aba4a7b8896488e87 |
| institution | Directory Open Access Journal |
| issn | 2090-9128 |
| language | English |
| last_indexed | 2024-12-20T13:05:32Z |
| publishDate | 2020-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of the Egyptian Mathematical Society |
| spelling | doaj.art-e1395525a0fe405aba4a7b8896488e872022-12-21T19:39:47ZengSpringerOpenJournal of the Egyptian Mathematical Society2090-91282020-08-0128111110.1186/s42787-020-00099-zTwo efficient methods for solving fractional Lane–Emden equations with conformable fractional derivativeAdyan M. Malik0Osama H. Mohammed1Dept. of Math. and Comp. Appl., Al-Nahrain UniversityDept. of Math. and Comp. Appl., Al-Nahrain UniversityAbstract In this paper, we introduce two reliable efficient approximate methods for solving a class of fractional Lane–Emden equations with conformable fractional derivative (CL-M) which are the so-called conformable Homotopy–Adomian decomposition method (CH-A) and conformable residual power series method (CRP). Furthermore, the proposed methods express the solutions of the non-linear cases of the CL-M in terms of fractional convergent series in which its components can be computed in an easy manner. Finally, the results are given by graphs for each case of the CL-M at different values of α in order to demonstrate its accuracy, applicability, and efficiency.http://link.springer.com/article/10.1186/s42787-020-00099-zFractional Lane–Emden equationsHAMResidual power series |
| spellingShingle | Adyan M. Malik Osama H. Mohammed Two efficient methods for solving fractional Lane–Emden equations with conformable fractional derivative Journal of the Egyptian Mathematical Society Fractional Lane–Emden equations HAM Residual power series |
| title | Two efficient methods for solving fractional Lane–Emden equations with conformable fractional derivative |
| title_full | Two efficient methods for solving fractional Lane–Emden equations with conformable fractional derivative |
| title_fullStr | Two efficient methods for solving fractional Lane–Emden equations with conformable fractional derivative |
| title_full_unstemmed | Two efficient methods for solving fractional Lane–Emden equations with conformable fractional derivative |
| title_short | Two efficient methods for solving fractional Lane–Emden equations with conformable fractional derivative |
| title_sort | two efficient methods for solving fractional lane emden equations with conformable fractional derivative |
| topic | Fractional Lane–Emden equations HAM Residual power series |
| url | http://link.springer.com/article/10.1186/s42787-020-00099-z |
| work_keys_str_mv | AT adyanmmalik twoefficientmethodsforsolvingfractionallaneemdenequationswithconformablefractionalderivative AT osamahmohammed twoefficientmethodsforsolvingfractionallaneemdenequationswithconformablefractionalderivative |