This work is devoted to the numerical treatment of the generalized Korteweg–de Vries–Burgers (GKdVB) equation involving a time–fractional derivative defined in the sense of the regularized Caputo–Prabhakar operator. To approximate the solution of this fractional nonlinear model, two meshless computational frameworks are employed. The first approach is the global radial basis function (GRBF) method, which utilizes globally supported basis functions to obtain highly accurate spatial approximations. The second approach is the radial basis function finite difference (RBF–FD) scheme, where the flexibility of radial basis functions is combined with the computational efficiency of finite difference–type discretizations.
These two strategies provide complementary advantages, balancing accuracy, computational efficiency, and adaptability to complex domains. A stability analysis of the resulting schemes is also presented to assess the reliability of the numerical approximations. To illustrate the performance of the proposed techniques, a representative numerical experiment is carried out, and the obtained results are reported through graphical and tabulated data. The numerical findings confirm that the GRBF and RBF–FD approaches provide accurate and stable approximations for the fractional GKdVB equation and demonstrate their potential for applications in various scientific and engineering problems involving nonlinear fractional models.
Irandoust-pakchin, S. , Dearkhshan, M. H. and Abdi-mazraeh, S. (2026). Numerical Methods for the Fractional Generalized Korteweg–de Vries–Burgers Equation with the Caputo–Prabhakar Derivative Using GRBF and RBF–FD Approaches. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2026.70096.3465
MLA
Irandoust-pakchin, S. , , Dearkhshan, M. H. , and Abdi-mazraeh, S. . "Numerical Methods for the Fractional Generalized Korteweg–de Vries–Burgers Equation with the Caputo–Prabhakar Derivative Using GRBF and RBF–FD Approaches", Computational Methods for Differential Equations, , , 2026, -. doi: 10.22034/cmde.2026.70096.3465
HARVARD
Irandoust-pakchin, S., Dearkhshan, M. H., Abdi-mazraeh, S. (2026). 'Numerical Methods for the Fractional Generalized Korteweg–de Vries–Burgers Equation with the Caputo–Prabhakar Derivative Using GRBF and RBF–FD Approaches', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2026.70096.3465
CHICAGO
S. Irandoust-pakchin , M. H. Dearkhshan and S. Abdi-mazraeh, "Numerical Methods for the Fractional Generalized Korteweg–de Vries–Burgers Equation with the Caputo–Prabhakar Derivative Using GRBF and RBF–FD Approaches," Computational Methods for Differential Equations, (2026): -, doi: 10.22034/cmde.2026.70096.3465
VANCOUVER
Irandoust-pakchin, S., Dearkhshan, M. H., Abdi-mazraeh, S. Numerical Methods for the Fractional Generalized Korteweg–de Vries–Burgers Equation with the Caputo–Prabhakar Derivative Using GRBF and RBF–FD Approaches. Computational Methods for Differential Equations, 2026; (): -. doi: 10.22034/cmde.2026.70096.3465
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