Revathy, J.M.Godavarma, G.2026-02-042024International Journal of Dynamics and Control, 2024, 12, 1, pp. 237-2452195268Xhttps://doi.org/10.1007/s40435-023-01237-yhttps://idr.nitk.ac.in/handle/123456789/21507Radial basis function-based finite difference (RBF-FD) schemes generalize finite difference methods, providing flexibility in node distribution as well as the shape of the domain. In this paper, we consider a numerical formulation based on RBF-FD for solving a time–space fractional diffusion problem defined using a fractional Laplacian operator. The model problem is simplified into a local problem in space using the Caffarelli–Silvestre extension method. The space derivatives in the resulting problem are then discretized using a local RBF-based finite difference method, while L1 approximation is used for the fractional time derivative. Results obtained using the proposed scheme are then compared with that given in the existing literature. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.Heat conductionImage segmentationLaplace transformsMathematical operatorsRadial basis function networksBase functionCaffarelli–silvestre extensionFinite-difference methodsFractional LaplacianFunctions approximationsL1 approximationLocal radial basis functionRadial base functionRadial basisSpace time fractional diffusion equationsFinite difference method