A Novel 2-Stage Fractional Runge–Kutta Method for a Time-Fractional Logistic Growth Model
In this paper, the fractional Euler method has been studied, and the derivation of the novel 2-stage fractional Runge–Kutta (FRK) method has been presented. The proposed fractional numerical method has been implemented to find the solution of fractional differential equations. The proposed novel met...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/1020472 |
| _version_ | 1797277635814883328 |
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| author | Muhammad Sarmad Arshad Dumitru Baleanu Muhammad Bilal Riaz Muhammad Abbas |
| author_facet | Muhammad Sarmad Arshad Dumitru Baleanu Muhammad Bilal Riaz Muhammad Abbas |
| author_sort | Muhammad Sarmad Arshad |
| collection | DOAJ |
| description | In this paper, the fractional Euler method has been studied, and the derivation of the novel 2-stage fractional Runge–Kutta (FRK) method has been presented. The proposed fractional numerical method has been implemented to find the solution of fractional differential equations. The proposed novel method will be helpful to derive the higher-order family of fractional Runge–Kutta methods. The nonlinear fractional Logistic Growth Model is solved and analyzed. The numerical results and graphs of the examples demonstrate the effectiveness of the method. |
| first_indexed | 2024-03-07T15:52:16Z |
| format | Article |
| id | doaj.art-5ed107806050422fa733aad63e427516 |
| institution | Directory Open Access Journal |
| issn | 1607-887X |
| language | English |
| last_indexed | 2024-03-07T15:52:16Z |
| publishDate | 2020-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj.art-5ed107806050422fa733aad63e4275162024-03-05T00:00:04ZengHindawi LimitedDiscrete Dynamics in Nature and Society1607-887X2020-01-01202010.1155/2020/10204721020472A Novel 2-Stage Fractional Runge–Kutta Method for a Time-Fractional Logistic Growth ModelMuhammad Sarmad Arshad0Dumitru Baleanu1Muhammad Bilal Riaz2Muhammad Abbas3Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsIn this paper, the fractional Euler method has been studied, and the derivation of the novel 2-stage fractional Runge–Kutta (FRK) method has been presented. The proposed fractional numerical method has been implemented to find the solution of fractional differential equations. The proposed novel method will be helpful to derive the higher-order family of fractional Runge–Kutta methods. The nonlinear fractional Logistic Growth Model is solved and analyzed. The numerical results and graphs of the examples demonstrate the effectiveness of the method.http://dx.doi.org/10.1155/2020/1020472 |
| spellingShingle | Muhammad Sarmad Arshad Dumitru Baleanu Muhammad Bilal Riaz Muhammad Abbas A Novel 2-Stage Fractional Runge–Kutta Method for a Time-Fractional Logistic Growth Model Discrete Dynamics in Nature and Society |
| title | A Novel 2-Stage Fractional Runge–Kutta Method for a Time-Fractional Logistic Growth Model |
| title_full | A Novel 2-Stage Fractional Runge–Kutta Method for a Time-Fractional Logistic Growth Model |
| title_fullStr | A Novel 2-Stage Fractional Runge–Kutta Method for a Time-Fractional Logistic Growth Model |
| title_full_unstemmed | A Novel 2-Stage Fractional Runge–Kutta Method for a Time-Fractional Logistic Growth Model |
| title_short | A Novel 2-Stage Fractional Runge–Kutta Method for a Time-Fractional Logistic Growth Model |
| title_sort | novel 2 stage fractional runge kutta method for a time fractional logistic growth model |
| url | http://dx.doi.org/10.1155/2020/1020472 |
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