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Ghomanjani, Fateme, Ansari, Khursheed. (1405). Bézier curve technique for solving p-fractional differential equations. سامانه مدیریت نشریات علمی, 14(4), 1546-1557. doi: 10.22034/cmde.2025.65612.3026
Fateme Ghomanjani; Khursheed J. Ansari. "Bézier curve technique for solving p-fractional differential equations". سامانه مدیریت نشریات علمی, 14, 4, 1405, 1546-1557. doi: 10.22034/cmde.2025.65612.3026
Ghomanjani, Fateme, Ansari, Khursheed. (1405). 'Bézier curve technique for solving p-fractional differential equations', سامانه مدیریت نشریات علمی, 14(4), pp. 1546-1557. doi: 10.22034/cmde.2025.65612.3026
Ghomanjani, Fateme, Ansari, Khursheed. Bézier curve technique for solving p-fractional differential equations. سامانه مدیریت نشریات علمی, 1405; 14(4): 1546-1557. doi: 10.22034/cmde.2025.65612.3026

Bézier curve technique for solving p-fractional differential equations

Computational Methods for Differential Equations
مقاله 2، دوره 14، شماره 4، دی 2026، صفحه 1546-1557    اصل مقاله (494.13 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.65612.3026
نویسندگان
Fateme Ghomanjani* 1؛ Khursheed J. Ansari* 2
1Department of Mathematics, Kashmar Higher Education Institute, Kashmar, Iran.
2Department of Mathematics, College of Science, King Khalid University, Abha, 61413, Saudi Arabia.
چکیده
The Bézier 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 mechanical frameworks. In this study, the stated Liouville-Caputo type $p$-fractional differential equation (pFDE) is solved by utilizing the Bézier curve method. Firstly, the $p$-fractional differential equation is transformed into the equivalent system of weakly singular $p$-integral equations by using several results of fractional $p$-calculus. Secondly, the Bézier curve method is used to solve the latter system of weakly singular $p$-integral equations. The stated method is an approximation technique that produces highly accurate results with minimal errors. Numerical examples are also given to check the validity of the BCM technique.
کلیدواژه‌ها
$p$-fractional differential equation؛ Bézier curve؛ $p$-fractional derivative؛ Simulation
مراجع
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