Analytical Methods for Fractional Differential Equations: Time-Fractional Foam Drainage and Fisher’s Equations
In this research, we employ a dual-approach that combines the Laplace residual power series method and the novel iteration method in conjunction with the Caputo operator. Our primary objective is to address the solution of two distinct, yet intricate partial differential equations: the Foam Drainage...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/10/1939 |
| _version_ | 1797572169664823296 |
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| author | Abdulrahman B. M. Alzahrani Ghadah Alhawael |
| author_facet | Abdulrahman B. M. Alzahrani Ghadah Alhawael |
| author_sort | Abdulrahman B. M. Alzahrani |
| collection | DOAJ |
| description | In this research, we employ a dual-approach that combines the Laplace residual power series method and the novel iteration method in conjunction with the Caputo operator. Our primary objective is to address the solution of two distinct, yet intricate partial differential equations: the Foam Drainage Equation and the nonlinear time-fractional Fisher’s equation. These equations, essential for modeling intricate processes, present analytical challenges due to their fractional derivatives and nonlinear characteristics. By amalgamating these distinctive methodologies, we derive precise and efficient solutions substantiated by comprehensive figures and tables showcasing the accuracy and reliability of our approach. Our study not only elucidates solutions to these equations, but also underscores the effectiveness of the Laplace Residual Power Series Method and the New Iteration Method as potent tools for grappling with intricate mathematical and physical models, thereby making significant contributions to advancements in diverse scientific domains. |
| first_indexed | 2024-03-10T20:51:36Z |
| format | Article |
| id | doaj.art-3a46c4e1f8594236b41a2c768f9c22e6 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T20:51:36Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-3a46c4e1f8594236b41a2c768f9c22e62023-11-19T18:19:03ZengMDPI AGSymmetry2073-89942023-10-011510193910.3390/sym15101939Analytical Methods for Fractional Differential Equations: Time-Fractional Foam Drainage and Fisher’s EquationsAbdulrahman B. M. Alzahrani0Ghadah Alhawael1Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaDepartment of Basic Sciences, Common First Year Deanship, King Saud University, P.O. Box 145111, Riyadh 11362, Saudi ArabiaIn this research, we employ a dual-approach that combines the Laplace residual power series method and the novel iteration method in conjunction with the Caputo operator. Our primary objective is to address the solution of two distinct, yet intricate partial differential equations: the Foam Drainage Equation and the nonlinear time-fractional Fisher’s equation. These equations, essential for modeling intricate processes, present analytical challenges due to their fractional derivatives and nonlinear characteristics. By amalgamating these distinctive methodologies, we derive precise and efficient solutions substantiated by comprehensive figures and tables showcasing the accuracy and reliability of our approach. Our study not only elucidates solutions to these equations, but also underscores the effectiveness of the Laplace Residual Power Series Method and the New Iteration Method as potent tools for grappling with intricate mathematical and physical models, thereby making significant contributions to advancements in diverse scientific domains.https://www.mdpi.com/2073-8994/15/10/1939Foam Drainage Equationnonlinear time-fractional Fisher’s equationLaplace Residual Power Series MethodNew Iteration MethodCaputo operatorfractional-order differential equation |
| spellingShingle | Abdulrahman B. M. Alzahrani Ghadah Alhawael Analytical Methods for Fractional Differential Equations: Time-Fractional Foam Drainage and Fisher’s Equations Symmetry Foam Drainage Equation nonlinear time-fractional Fisher’s equation Laplace Residual Power Series Method New Iteration Method Caputo operator fractional-order differential equation |
| title | Analytical Methods for Fractional Differential Equations: Time-Fractional Foam Drainage and Fisher’s Equations |
| title_full | Analytical Methods for Fractional Differential Equations: Time-Fractional Foam Drainage and Fisher’s Equations |
| title_fullStr | Analytical Methods for Fractional Differential Equations: Time-Fractional Foam Drainage and Fisher’s Equations |
| title_full_unstemmed | Analytical Methods for Fractional Differential Equations: Time-Fractional Foam Drainage and Fisher’s Equations |
| title_short | Analytical Methods for Fractional Differential Equations: Time-Fractional Foam Drainage and Fisher’s Equations |
| title_sort | analytical methods for fractional differential equations time fractional foam drainage and fisher s equations |
| topic | Foam Drainage Equation nonlinear time-fractional Fisher’s equation Laplace Residual Power Series Method New Iteration Method Caputo operator fractional-order differential equation |
| url | https://www.mdpi.com/2073-8994/15/10/1939 |
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