Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran.
10.22034/cmde.2025.68697.3347
Abstract
Considering the significant applications of fractional differential equations, their numerical solutions hold particular importance. Meshless methods have been employed by researchers for numerically solving these equations, which are often of integer order in the spatial dimension. However, the governing equation in this paper involves the spatial fractional derivative of the Riesz type and a singular Hadamard-type in spatial and time dimensions, respectively. Instead of deriving the global weak form of the problem, we utilize their weak form over local subdomains. In this study, for the first time, we calculate the Riesz-type fractional derivatives of the shape functions of the moving Kriging interpolation method and use them to discretize the reaction diffusion equation in the spatial dimension. The finite difference method is then applied to discretize the problem in the temporal dimension. We also conduct a convergence analysis, which demonstrates that the temporal order of the method is O(τ). To evaluate the accuracy and capability of the present scheme, three numerical examples are tested, and the results indicate high accuracy.
Habibirad, A. and Ordokhani, Y. (2026). A novel meshless technique based on generalized moving Kriging interpolation for Caputo-Hadamard time and Riesz space fractional reaction-diffusion equation. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2025.68697.3347
MLA
Habibirad, A. , and Ordokhani, Y. . "A novel meshless technique based on generalized moving Kriging interpolation for Caputo-Hadamard time and Riesz space fractional reaction-diffusion equation", Computational Methods for Differential Equations, , , 2026, -. doi: 10.22034/cmde.2025.68697.3347
HARVARD
Habibirad, A., Ordokhani, Y. (2026). 'A novel meshless technique based on generalized moving Kriging interpolation for Caputo-Hadamard time and Riesz space fractional reaction-diffusion equation', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2025.68697.3347
CHICAGO
A. Habibirad and Y. Ordokhani, "A novel meshless technique based on generalized moving Kriging interpolation for Caputo-Hadamard time and Riesz space fractional reaction-diffusion equation," Computational Methods for Differential Equations, (2026): -, doi: 10.22034/cmde.2025.68697.3347
VANCOUVER
Habibirad, A., Ordokhani, Y. A novel meshless technique based on generalized moving Kriging interpolation for Caputo-Hadamard time and Riesz space fractional reaction-diffusion equation. Computational Methods for Differential Equations, 2026; (): -. doi: 10.22034/cmde.2025.68697.3347
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