Bézier curve technique for solving p-fractional differential equations

Ghomanjani, Fateme; Ansari, Khursheed J.

doi:10.22034/cmde.2025.65612.3026

Bézier curve technique for solving p-fractional differential equations

Document Type : Research Paper

Authors

¹ Department of Mathematics, Kashmar Higher Education Institute, Kashmar, Iran.

² Department of Mathematics, College of Science, King Khalid University, Abha, 61413, Saudi Arabia.

10.22034/cmde.2025.65612.3026

Abstract

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.

Keywords

Main Subjects

Numerical methods for ordinary differential equations

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