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Computational analysis of fractal-fractional differential systems via Vieta-Lucas fractal-fractional operational matrices | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 28 فروردین 1405 اصل مقاله (2.12 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.66734.3149 | ||
| نویسندگان | ||
| Rakesh Kumar1؛ Shivani Aeri* 1؛ Dumitru Baleanu2 | ||
| 1School of Mathematics, Computers and Information Sciences, Central University of Himachal Pradesh, Shahpur Campus, Shahpur 176206, India. | ||
| 2Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon. | ||
| چکیده | ||
| Fractal-fractional differential equations are important as they can help to model the real-world systems that have memory effects and thus find their existence in various real-world phenomena such as physics, engineering, biology, and biomedicine. It is always challenging to handle the fractal-fractional derivatives using traditional numerical methods, which motivates the need to develop the numerical methods that can handle these fractal-fractional models accurately and effectively. In this work, a novel numerical scheme, the Vieta-Lucas fractal fractional matrix (VLFF) method, is presented for solving the system of fractal-fractional differential equations (FFDEs). The operational matrices for derivative and fractal fractional derivatives of Vieta-Lucas polynomials over the generalized domain are constructed. Making use of the fractal-fractional operational matrix technique streamlines the computation processes and significantly reduces the challenges while dealing with fractal-fractional derivatives. This simplified matrix method is then applied with the Tau approach to find the solution of a system of FFDEs. Further, the geometric representation of the fractal-fractional derivative matrix is presented, showcasing the fractal patterns. The proposed method is validated through numerous examples, with solution curves and error analysis presented for different fractal and fractional orders. A comparison has been made with the existing numerical methods to validate the accuracy and reliability of the proposed VLFF method. | ||
| کلیدواژهها | ||
| Fractal-fractional differential equations؛ Vieta-Lucas polynomials؛ Operation matrix؛ Tau method؛ Numerical solution | ||
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