Exploring new routes in fractional modeling: analytical solutions of Burgers-type systems via Caputo-Hadamard and ϕ-Caputo derivatives
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| Pubblicato in: | Boundary Value Problems vol. 2025, no. 1 (Dec 2025), p. 166 |
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| Altri autori: | , , , , , |
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Hindawi Limited
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| Accesso online: | Citation/Abstract Full Text Full Text - PDF |
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| 045 | 2 | |b d20251201 |b d20251231 | |
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| 100 | 1 | |a Alshammari, Mohammad |u University of Ha’il, Department of Mathematics, College of Science, Ha’il, Saudi Arabia (GRID:grid.443320.2) (ISNI:0000 0004 0608 0056) | |
| 245 | 1 | |a Exploring new routes in fractional modeling: analytical solutions of Burgers-type systems via Caputo-Hadamard and <i>ϕ</i>-Caputo derivatives | |
| 260 | |b Hindawi Limited |c Dec 2025 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a The study of fractional-order partial differential equations has gained significant attention due to its ability to model complex physical systems with memory effects and hereditary properties. Among these systems is the Burgers equation, which serves as a fundamental model for describing nonlinear waves, turbulence, and the behavior of viscous fluids. Recent advancements in fractional calculus have led to the development of generalized fractional operators, such as the Caputo-Hadamard and ϕ-Caputo fractional derivatives. These operators offer greater flexibility and precision in capturing temporal and spatial nonlocal effects. This paper provides a comprehensive review of analytical and semi-analytical methods for solving these systems, with a particular emphasis on the Residual Power Series Method (RPSM) and the New Iterative Method (NIM). Both methods demonstrate superior convergence rates and accuracy. By combining generalized fractional operators with iterative algorithms, new approaches can be developed to model real-world phenomena in fields like physics, engineering, and applied mathematics. This work not only summarizes recent progress but also establishes a strong foundation for future research into complex fractional-order systems. | |
| 653 | |a Calculus | ||
| 653 | |a Iterative algorithms | ||
| 653 | |a Partial differential equations | ||
| 653 | |a Mathematical analysis | ||
| 653 | |a Iterative methods | ||
| 653 | |a Operators (mathematics) | ||
| 653 | |a Applications of mathematics | ||
| 653 | |a Power series | ||
| 653 | |a Fluid flow | ||
| 653 | |a Exact solutions | ||
| 653 | |a Methods | ||
| 653 | |a Fractional calculus | ||
| 653 | |a Algorithms | ||
| 653 | |a Burgers equation | ||
| 653 | |a Viscous fluids | ||
| 653 | |a Derivatives | ||
| 700 | 1 | |a Alshammari, Tariq S. |u University of Ha’il, Department of Mathematics, College of Science, Ha’il, Saudi Arabia (GRID:grid.443320.2) (ISNI:0000 0004 0608 0056) | |
| 700 | 1 | |a Alshammari, Saleh |u University of Ha’il, Department of Mathematics, College of Science, Ha’il, Saudi Arabia (GRID:grid.443320.2) (ISNI:0000 0004 0608 0056) | |
| 700 | 1 | |a Alsheekhhussain, Zainab |u University of Ha’il, Department of Mathematics, College of Science, Ha’il, Saudi Arabia (GRID:grid.443320.2) (ISNI:0000 0004 0608 0056) | |
| 700 | 1 | |a Shah, Rasool |u Abdul Wali Khan University Mardan, Department of Mathematics, Mardan, Pakistan (GRID:grid.440522.5) (ISNI:0000 0004 0478 6450) | |
| 700 | 1 | |a Jebran, Samaruddin |u Kabul University, Faculty of Mathematics, Kabul, Afghanistan (GRID:grid.442864.8) (ISNI:0000 0001 1181 4542) | |
| 700 | 1 | |a Al-sawalha, M. Mossa |u University of Ha’il, Department of Mathematics, College of Science, Ha’il, Saudi Arabia (GRID:grid.443320.2) (ISNI:0000 0004 0608 0056) | |
| 773 | 0 | |t Boundary Value Problems |g vol. 2025, no. 1 (Dec 2025), p. 166 | |
| 786 | 0 | |d ProQuest |t Advanced Technologies & Aerospace Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3270621309/abstract/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text |u https://www.proquest.com/docview/3270621309/fulltext/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3270621309/fulltextPDF/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |