Novel Approximations to the Multi-Dimensional Fractional Diffusion Models Using the Tantawy Technique and Two Other Transformed Methods
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| Publicado en: | Fractal and Fractional vol. 9, no. 7 (2025), p. 423-471 |
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MDPI AG
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| Acceso en línea: | Citation/Abstract Full Text + Graphics Full Text - PDF |
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| 001 | 3233189461 | ||
| 003 | UK-CbPIL | ||
| 022 | |a 2504-3110 | ||
| 024 | 7 | |a 10.3390/fractalfract9070423 |2 doi | |
| 035 | |a 3233189461 | ||
| 045 | 2 | |b d20250101 |b d20251231 | |
| 100 | 1 | |a Weaam, Alhejaili |u Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia | |
| 245 | 1 | |a Novel Approximations to the Multi-Dimensional Fractional Diffusion Models Using the Tantawy Technique and Two Other Transformed Methods | |
| 260 | |b MDPI AG |c 2025 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a This study analyzes the family of one of the most essential fractional differential equations due to its wide applications in physics and engineering: the multidimensional fractional linear and nonlinear diffusion equations. The Caputo fractional derivative operator is used to treat the time-fractional derivative. To complete the analysis and generate more stable and highly accurate approximations of the proposed models, three extremely effective techniques, known as the direct Tantawy technique, the new iterative transform technique (NITM), and the homotopy perturbation transform method (HPTM), which combine the Elzaki transform (ET) with the new iterative method (NIM), and the homotopy perturbation method (HPM), are employed. These reliable approaches produce more stable and highly accurate analytical approximations in series form, which converge to the exact solutions after a few iterations. As the number of terms/iterations in the problems series solution rises, it is found that the derived approximations are closely related to each problem’s exact solutions. The two- and three-dimensional graphical representations are considered to understand the mechanism and dynamics of the nonlinear phenomena described by the derived approximations. Moreover, both the absolute and residual errors for all generated approximations are estimated to demonstrate the high accuracy of all derived approximations. The obtained results are encouraging and appropriate for investigating diffusion problems. The primary benefit lies in the fact that our proposed plan does not necessitate any presumptions or limitations on variables that might affect the real problems. One of the most essential features of the proposed methods is the low computational cost and fast computations, especially for the Tantawy technique. The findings of the present study will be valuable as a tool for handling fractional partial differential equation solutions. These approaches are essential in solving the problem and moving beyond the restrictions on variables that could make modeling the problem challenging. | |
| 653 | |a Calculus | ||
| 653 | |a Physics | ||
| 653 | |a Partial differential equations | ||
| 653 | |a Mathematical analysis | ||
| 653 | |a Iterative methods | ||
| 653 | |a Operators (mathematics) | ||
| 653 | |a Exact solutions | ||
| 653 | |a Approximation | ||
| 653 | |a Mathematical models | ||
| 653 | |a Methods | ||
| 653 | |a Fractional calculus | ||
| 653 | |a Graphical representations | ||
| 653 | |a Nonlinear dynamics | ||
| 653 | |a Perturbation methods | ||
| 653 | |a Nonlinear phenomena | ||
| 653 | |a Derivatives | ||
| 653 | |a COVID-19 | ||
| 700 | 1 | |a Khan, Adnan |u Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan | |
| 700 | 1 | |a Al-Johani, Amnah S |u Mathematics Department, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia | |
| 700 | 1 | |a El-Tantawy, Samir A |u Department of Physics, Faculty of Science, Port Said University, Port Said 42521, Egypt | |
| 773 | 0 | |t Fractal and Fractional |g vol. 9, no. 7 (2025), p. 423-471 | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3233189461/abstract/embedded/75I98GEZK8WCJMPQ?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text + Graphics |u https://www.proquest.com/docview/3233189461/fulltextwithgraphics/embedded/75I98GEZK8WCJMPQ?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3233189461/fulltextPDF/embedded/75I98GEZK8WCJMPQ?source=fedsrch |