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B\'{e}zier Curve Technique for Solving $p$-fractional Differential Equations | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 03 شهریور 1404 اصل مقاله (1.26 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.65612.3026 | ||
| نویسندگان | ||
| Khursheed J. Ansari* 1؛ Fateme Ghomanjani2 | ||
| 1Department of Mathematics, College of Science, King Khalid University, Abha, 61413, Saudi Arabia. | ||
| 2Department of Mathematics, Kashmar Higher Education Institute, Kashmar, Iran. | ||
| چکیده | ||
| The B'ezier curve technique is a numerical method often adopted for solving complex differential equations, including fractional differential equations. The quantum analogue of fractional differential equations extends classical fractional differential equations into the quantum domain, involving fractional calculus within quantum mechanic frameworks. In this sequel, the stated Liouville-Caputo type $p$-fractional differential equation ( pFDE ) is solved by utilizing the B'{e}zier curve method. Firstly, the $p$-fractional differential equation is transformed into the equivalent systems of weakly singular $p$-integral equations by many results of fractional $p$-calculus. Secondly, the B'{e}zier curve method is used to solve the latter systems of weakly singular $p$-integral equations. The stated method is an approximation method which has very small errors as it gives very good results. Numerical examples are also given to check the validity of the BCM technique. | ||
| کلیدواژه‌ها | ||
| $p$-fractional differential equation؛ B\'{e}zier curve؛ $p$-fractional derivative؛ Simulation | ||
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آمار تعداد مشاهده مقاله: 52 تعداد دریافت فایل اصل مقاله: 63 |
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