On the Fractional View Analysis of Keller–Segel Equations with Sensitivity Functions
In this paper, the fractional view analysis of the Keller–Segal equations with sensitivity functions is presented. The Caputo operator has been used to pursue the present research work. The natural transform is combined with the homotopy perturbation method, and a new scheme for implementation is de...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/2371019 |
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| _version_ | 1832566326203252736 |
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| author | Haobin Liu Hassan Khan Rasool Shah A. A. Alderremy Shaban Aly Dumitru Baleanu |
| author_facet | Haobin Liu Hassan Khan Rasool Shah A. A. Alderremy Shaban Aly Dumitru Baleanu |
| author_sort | Haobin Liu |
| collection | DOAJ |
| description | In this paper, the fractional view analysis of the Keller–Segal equations with sensitivity functions is presented. The Caputo operator has been used to pursue the present research work. The natural transform is combined with the homotopy perturbation method, and a new scheme for implementation is derived. The modified established method is named as the homotopy perturbation transform technique. The derived results are compared with the solution of the Laplace Adomian decomposition technique by using the systems of fractional Keller–Segal equations. The solution graphs and the table have shown that the obtained results coincide with the solution of the Laplace Adomian decomposition method. Fractional-order solutions are determined to confirm the reliability of the current method. It is observed that the solutions at various fractional orders are convergent to an integer-order solution of the problems. The suggested procedure is very attractive and straight forward and therefore can be modified to solve high nonlinear fractional partial differential equations and their systems. |
| format | Article |
| id | doaj-art-269c8bf6284b4a4db7f8deaaa2b2f301 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-269c8bf6284b4a4db7f8deaaa2b2f3012025-02-03T01:04:28ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/23710192371019On the Fractional View Analysis of Keller–Segel Equations with Sensitivity FunctionsHaobin Liu0Hassan Khan1Rasool Shah2A. A. Alderremy3Shaban Aly4Dumitru Baleanu5Data Recovery Key Laboratory of Sichuan Province, Neijiang Normal University, Neijiang 641000, Sichuan, ChinaDepartment of Mathematics, Abdul Wali Khan University Mardan (AWKUM), Mardan, PakistanDepartment of Mathematics, Abdul Wali Khan University Mardan (AWKUM), Mardan, PakistanDepartment of Mathematics, Faculty of Science, King Khalid University, Abha 61413, Saudi ArabiaDepartment of Mathematics, Faculty of Science, AL-Azhar University, Assiu, 71516, EgyptDepartment of Mathematics, Faculty of Arts and Sciences, Cankaya University, Ankara 06530, TurkeyIn this paper, the fractional view analysis of the Keller–Segal equations with sensitivity functions is presented. The Caputo operator has been used to pursue the present research work. The natural transform is combined with the homotopy perturbation method, and a new scheme for implementation is derived. The modified established method is named as the homotopy perturbation transform technique. The derived results are compared with the solution of the Laplace Adomian decomposition technique by using the systems of fractional Keller–Segal equations. The solution graphs and the table have shown that the obtained results coincide with the solution of the Laplace Adomian decomposition method. Fractional-order solutions are determined to confirm the reliability of the current method. It is observed that the solutions at various fractional orders are convergent to an integer-order solution of the problems. The suggested procedure is very attractive and straight forward and therefore can be modified to solve high nonlinear fractional partial differential equations and their systems.http://dx.doi.org/10.1155/2020/2371019 |
| spellingShingle | Haobin Liu Hassan Khan Rasool Shah A. A. Alderremy Shaban Aly Dumitru Baleanu On the Fractional View Analysis of Keller–Segel Equations with Sensitivity Functions Complexity |
| title | On the Fractional View Analysis of Keller–Segel Equations with Sensitivity Functions |
| title_full | On the Fractional View Analysis of Keller–Segel Equations with Sensitivity Functions |
| title_fullStr | On the Fractional View Analysis of Keller–Segel Equations with Sensitivity Functions |
| title_full_unstemmed | On the Fractional View Analysis of Keller–Segel Equations with Sensitivity Functions |
| title_short | On the Fractional View Analysis of Keller–Segel Equations with Sensitivity Functions |
| title_sort | on the fractional view analysis of keller segel equations with sensitivity functions |
| url | http://dx.doi.org/10.1155/2020/2371019 |
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