Analytical simulation of the nonlinear Caputo fractional equations
Partial differential equations (PDEs), particularly those involving fractional derivatives, have garnered considerable attention due to their ability to model complex systems with memory and hereditary properties. This paper focuses on the generalized Caputo fractional equation and presents a compar...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-09-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818125001913 |
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| author | Ali Ahadi Seyed Mostafa Mousavi Amir Mohammad Alinia Hossein Khademi |
| author_facet | Ali Ahadi Seyed Mostafa Mousavi Amir Mohammad Alinia Hossein Khademi |
| author_sort | Ali Ahadi |
| collection | DOAJ |
| description | Partial differential equations (PDEs), particularly those involving fractional derivatives, have garnered considerable attention due to their ability to model complex systems with memory and hereditary properties. This paper focuses on the generalized Caputo fractional equation and presents a comparative analysis of three powerful solution techniques: the Homotopy Perturbation Method (HPM), the Variational Iteration Method (VIM), and the Akbari-Ganji Method (AGM). These methods are applied to fractional differential equations (FDEs) to derive approximate solutions. The accuracy and effectiveness of the methods are demonstrated through detailed comparisons with exact solutions and previous works in the field.The study highlights the strengths of each technique in handling non-linear and fractional-order problems, providing reliable results with minimal error. Specifically, the HPM and VIM show remarkable convergence properties, while the AGM proves efficient in solving both linear and non-linear equations. These methods are validated by comparing the results with known solutions, which shows that these techniques work for a wide range of FDEs. The present study underscores the applicability of these approaches in several scientific and technological domains, hence promoting more advancements in the numerical examination of fractional systems. |
| format | Article |
| id | doaj-art-5adf3867b6494fd3aa3e31dbae862f3e |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-5adf3867b6494fd3aa3e31dbae862f3e2025-08-20T03:56:17ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-09-011510126410.1016/j.padiff.2025.101264Analytical simulation of the nonlinear Caputo fractional equationsAli Ahadi0Seyed Mostafa Mousavi1Amir Mohammad Alinia2Hossein Khademi3Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, Iran; Corresponding author.Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, IranDepartment of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, IranDepartment of Electrical Engineering, Faculty of Technology and Engineering, University of Mazandaran, Babolsar, IranPartial differential equations (PDEs), particularly those involving fractional derivatives, have garnered considerable attention due to their ability to model complex systems with memory and hereditary properties. This paper focuses on the generalized Caputo fractional equation and presents a comparative analysis of three powerful solution techniques: the Homotopy Perturbation Method (HPM), the Variational Iteration Method (VIM), and the Akbari-Ganji Method (AGM). These methods are applied to fractional differential equations (FDEs) to derive approximate solutions. The accuracy and effectiveness of the methods are demonstrated through detailed comparisons with exact solutions and previous works in the field.The study highlights the strengths of each technique in handling non-linear and fractional-order problems, providing reliable results with minimal error. Specifically, the HPM and VIM show remarkable convergence properties, while the AGM proves efficient in solving both linear and non-linear equations. These methods are validated by comparing the results with known solutions, which shows that these techniques work for a wide range of FDEs. The present study underscores the applicability of these approaches in several scientific and technological domains, hence promoting more advancements in the numerical examination of fractional systems.http://www.sciencedirect.com/science/article/pii/S2666818125001913Fractional differential equationsPartial differential equationsCaputo fractional equationHomotopy Perturbation Method |
| spellingShingle | Ali Ahadi Seyed Mostafa Mousavi Amir Mohammad Alinia Hossein Khademi Analytical simulation of the nonlinear Caputo fractional equations Partial Differential Equations in Applied Mathematics Fractional differential equations Partial differential equations Caputo fractional equation Homotopy Perturbation Method |
| title | Analytical simulation of the nonlinear Caputo fractional equations |
| title_full | Analytical simulation of the nonlinear Caputo fractional equations |
| title_fullStr | Analytical simulation of the nonlinear Caputo fractional equations |
| title_full_unstemmed | Analytical simulation of the nonlinear Caputo fractional equations |
| title_short | Analytical simulation of the nonlinear Caputo fractional equations |
| title_sort | analytical simulation of the nonlinear caputo fractional equations |
| topic | Fractional differential equations Partial differential equations Caputo fractional equation Homotopy Perturbation Method |
| url | http://www.sciencedirect.com/science/article/pii/S2666818125001913 |
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