B\'{e}zier Curve Technique for Solving $p$-fractional Differential Equations

Articles in Press

Document Type : Research Paper

Authors

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

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

Abstract

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.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 25 August 2025

Files

History

  • Receive Date: 25 January 2025
  • Revise Date: 28 June 2025
  • Accept Date: 24 August 2025

Share

How to cite

Statistics