Hybrid technique for multi-dimensional fractional diffusion problems involving Caputo–Fabrizio derivative
In this study, a precise and analytical method, namely Shehu transform decomposition method (STDM), is applied to examine multi-dimensional fractional diffusion equations, which will describe density dynamics in a material undergoing diffusion. The fractional derivative is taken into account by the...
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
World Scientific Publishing
2024-12-01
|
| Series: | International Journal of Mathematics for Industry |
| Subjects: | |
| Online Access: | https://www.worldscientific.com/doi/10.1142/S2661335224500205 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832576359311867904 |
|---|---|
| author | Surendar Kumar Yadav Mridula Purohit Murli Manohar Gour Lokesh Kumar Yadav Manvendra Narayan Mishra |
| author_facet | Surendar Kumar Yadav Mridula Purohit Murli Manohar Gour Lokesh Kumar Yadav Manvendra Narayan Mishra |
| author_sort | Surendar Kumar Yadav |
| collection | DOAJ |
| description | In this study, a precise and analytical method, namely Shehu transform decomposition method (STDM), is applied to examine multi-dimensional fractional diffusion equations, which will describe density dynamics in a material undergoing diffusion. The fractional derivative is taken into account by the Caputo–Fabrizio (CF) derivative. The proposed approach combines the Shehu transformation (ST) with the Adomian decomposition method (ADM), employing Adomain polynomials to handle nonlinear terms. Fixed point theorem has been used to prove the uniqueness and existence of the solution of governing differential equation. To validate the accuracy of proposed method, we present the analytical solutions of three applications of multi-dimensional fractional diffusion equations. Furthermore, we compute the graphical and numerical results using MATLAB to demonstrate the close-form analytical solution in the comparison of the exact solution. The obtained findings are promising and suitable for the solution of multi-dimensional diffusion problems with time-fractional derivatives. The main advantage is that our developed scheme does not require assumptions or restrictions on variables that ruin the actual problem. This scheme plays a significant role in finding the solution and overcoming the restriction of variables that may cause difficulty in modeling the problem. |
| format | Article |
| id | doaj-art-ae73ad3b06924476a1d8f29e53e68118 |
| institution | Kabale University |
| issn | 2661-3352 2661-3344 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | World Scientific Publishing |
| record_format | Article |
| series | International Journal of Mathematics for Industry |
| spelling | doaj-art-ae73ad3b06924476a1d8f29e53e681182025-01-31T06:15:29ZengWorld Scientific PublishingInternational Journal of Mathematics for Industry2661-33522661-33442024-12-01160110.1142/S2661335224500205Hybrid technique for multi-dimensional fractional diffusion problems involving Caputo–Fabrizio derivativeSurendar Kumar Yadav0Mridula Purohit1Murli Manohar Gour2Lokesh Kumar Yadav3Manvendra Narayan Mishra4Department of Mathematics, Vivekananda Global University, Jaipur, Rajasthan, IndiaDepartment of Mathematics, Vivekananda Global University, Jaipur, Rajasthan, IndiaDepartment of Mathematics, Vivekananda Global University, Jaipur, Rajasthan, IndiaDepartment of Mathematics, Vivekananda Global University, Jaipur, Rajasthan, IndiaDepartment of Mathematics, Suresh Gyan Vihar University, Jaipur, Rajasthan, IndiaIn this study, a precise and analytical method, namely Shehu transform decomposition method (STDM), is applied to examine multi-dimensional fractional diffusion equations, which will describe density dynamics in a material undergoing diffusion. The fractional derivative is taken into account by the Caputo–Fabrizio (CF) derivative. The proposed approach combines the Shehu transformation (ST) with the Adomian decomposition method (ADM), employing Adomain polynomials to handle nonlinear terms. Fixed point theorem has been used to prove the uniqueness and existence of the solution of governing differential equation. To validate the accuracy of proposed method, we present the analytical solutions of three applications of multi-dimensional fractional diffusion equations. Furthermore, we compute the graphical and numerical results using MATLAB to demonstrate the close-form analytical solution in the comparison of the exact solution. The obtained findings are promising and suitable for the solution of multi-dimensional diffusion problems with time-fractional derivatives. The main advantage is that our developed scheme does not require assumptions or restrictions on variables that ruin the actual problem. This scheme plays a significant role in finding the solution and overcoming the restriction of variables that may cause difficulty in modeling the problem.https://www.worldscientific.com/doi/10.1142/S2661335224500205Multi-dimensional fractional diffusion problemsAdomain polynomialsShehu transformnon-singular fractional derivative |
| spellingShingle | Surendar Kumar Yadav Mridula Purohit Murli Manohar Gour Lokesh Kumar Yadav Manvendra Narayan Mishra Hybrid technique for multi-dimensional fractional diffusion problems involving Caputo–Fabrizio derivative International Journal of Mathematics for Industry Multi-dimensional fractional diffusion problems Adomain polynomials Shehu transform non-singular fractional derivative |
| title | Hybrid technique for multi-dimensional fractional diffusion problems involving Caputo–Fabrizio derivative |
| title_full | Hybrid technique for multi-dimensional fractional diffusion problems involving Caputo–Fabrizio derivative |
| title_fullStr | Hybrid technique for multi-dimensional fractional diffusion problems involving Caputo–Fabrizio derivative |
| title_full_unstemmed | Hybrid technique for multi-dimensional fractional diffusion problems involving Caputo–Fabrizio derivative |
| title_short | Hybrid technique for multi-dimensional fractional diffusion problems involving Caputo–Fabrizio derivative |
| title_sort | hybrid technique for multi dimensional fractional diffusion problems involving caputo fabrizio derivative |
| topic | Multi-dimensional fractional diffusion problems Adomain polynomials Shehu transform non-singular fractional derivative |
| url | https://www.worldscientific.com/doi/10.1142/S2661335224500205 |
| work_keys_str_mv | AT surendarkumaryadav hybridtechniqueformultidimensionalfractionaldiffusionproblemsinvolvingcaputofabrizioderivative AT mridulapurohit hybridtechniqueformultidimensionalfractionaldiffusionproblemsinvolvingcaputofabrizioderivative AT murlimanohargour hybridtechniqueformultidimensionalfractionaldiffusionproblemsinvolvingcaputofabrizioderivative AT lokeshkumaryadav hybridtechniqueformultidimensionalfractionaldiffusionproblemsinvolvingcaputofabrizioderivative AT manvendranarayanmishra hybridtechniqueformultidimensionalfractionaldiffusionproblemsinvolvingcaputofabrizioderivative |