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  4. Numerical solution for fractional differential equations by using Jacobi–Gauss–Radau collocation method

Numerical solution for fractional differential equations by using Jacobi–Gauss–Radau collocation method

MMC.
2025;
Volume 12, Number 2
: pp. 661–668
https://doi.org/10.23939/mmc2025.02.661
Received: December 27, 2024
Accepted: June 21, 2025

Hussain A. K., Alghamdi A. S., Alzaidy J. F., Hussain A. H., Abdul Rahman N. A.  Numerical solution for fractional differential equations by using Jacobi–Gauss–Radau collocation method.  Mathematical Modeling and Computing. Vol. 12, No. 2, pp. 661–668 (2025)

Authors:
  1. A. K. Hussain
  2. A. S. Alghamdi
  3. J. F. Alzaidy
  4. A. H. Hussain
  5. N. A. Abdul Rahman
1
Department of Material Engineering, Mustansiriyah University
2
Department of Mathematics, Faculty of Science, AlBaha University
3
Department of Mathematics, Faculty of Science, King Abdulaziz University
4
Department of Automobile Engineering, College of Engineering Al-Musayab, University of Babylon
5
School of Mathematical Sciences, Universiti Sains Malaysia

This study proposes a novel numerical approach for addressing both linear and nonlinear initial fractional order differential equations (FDEs) through the implementation of the Jacobi–Gauss–Radau (JGR) integrated with Caputo fractional derivatives.  The problem is effectively transformed into a simplified system of FDEs, encompassing the unknown coefficients, by employing shifted JGR points for the FDEs and their initial conditions.  For the purpose of investigating the effectiveness and accuracy of the introduced method, some numerical illustrations are provided for various linear and nonlinear FDEs.

fractional differential equations
numerical solution
Jacobi–Gauss–Radau
collocation method
spectral methods
fractional calculus
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