Advanced Analytical Treatment of Fractional Logistic Equations Based on Residual Error Functions
In this article, an analytical reliable treatment based on the concept of residual error functions is employed to address the series solution of the differential logistic system in the fractional sense. The proposed technique is a combination of the generalized Taylor series and minimizing the resid...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2019/7609879 |
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| _version_ | 1832565642503389184 |
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| author | Saleh Alshammari Mohammed Al-Smadi Mohammad Al Shammari Ishak Hashim Mohd Almie Alias |
| author_facet | Saleh Alshammari Mohammed Al-Smadi Mohammad Al Shammari Ishak Hashim Mohd Almie Alias |
| author_sort | Saleh Alshammari |
| collection | DOAJ |
| description | In this article, an analytical reliable treatment based on the concept of residual error functions is employed to address the series solution of the differential logistic system in the fractional sense. The proposed technique is a combination of the generalized Taylor series and minimizing the residual error function. The solution methodology depends on the generation of a fractional expansion in an effective convergence formula, as well as on the optimization of truncated errors, Resqjt, through the use of repeated Caputo derivatives without any restrictive assumptions of system nature. To achieve this, some logistic patterns are tested to demonstrate the reliability and applicability of the suggested approach. Numerical comparison depicts that the proposed technique has high accuracy and less computational effect and is more efficient. |
| format | Article |
| id | doaj-art-455814007c3547d9b6dc98d308f7fa48 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-455814007c3547d9b6dc98d308f7fa482025-02-03T01:07:02ZengWileyInternational Journal of Differential Equations1687-96431687-96512019-01-01201910.1155/2019/76098797609879Advanced Analytical Treatment of Fractional Logistic Equations Based on Residual Error FunctionsSaleh Alshammari0Mohammed Al-Smadi1Mohammad Al Shammari2Ishak Hashim3Mohd Almie Alias4Centre for Modelling and Data Science, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, MalaysiaDepartment of Applied Science, Ajloun College, Al-Balqa Applied University, Ajloun 26816, JordanCentre for Modelling and Data Science, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, MalaysiaCentre for Modelling and Data Science, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, MalaysiaCentre for Modelling and Data Science, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, MalaysiaIn this article, an analytical reliable treatment based on the concept of residual error functions is employed to address the series solution of the differential logistic system in the fractional sense. The proposed technique is a combination of the generalized Taylor series and minimizing the residual error function. The solution methodology depends on the generation of a fractional expansion in an effective convergence formula, as well as on the optimization of truncated errors, Resqjt, through the use of repeated Caputo derivatives without any restrictive assumptions of system nature. To achieve this, some logistic patterns are tested to demonstrate the reliability and applicability of the suggested approach. Numerical comparison depicts that the proposed technique has high accuracy and less computational effect and is more efficient.http://dx.doi.org/10.1155/2019/7609879 |
| spellingShingle | Saleh Alshammari Mohammed Al-Smadi Mohammad Al Shammari Ishak Hashim Mohd Almie Alias Advanced Analytical Treatment of Fractional Logistic Equations Based on Residual Error Functions International Journal of Differential Equations |
| title | Advanced Analytical Treatment of Fractional Logistic Equations Based on Residual Error Functions |
| title_full | Advanced Analytical Treatment of Fractional Logistic Equations Based on Residual Error Functions |
| title_fullStr | Advanced Analytical Treatment of Fractional Logistic Equations Based on Residual Error Functions |
| title_full_unstemmed | Advanced Analytical Treatment of Fractional Logistic Equations Based on Residual Error Functions |
| title_short | Advanced Analytical Treatment of Fractional Logistic Equations Based on Residual Error Functions |
| title_sort | advanced analytical treatment of fractional logistic equations based on residual error functions |
| url | http://dx.doi.org/10.1155/2019/7609879 |
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