KAUST DepartmentApplied Mathematics and Computational Science Program
Computational Bioscience Research Center (CBRC)
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Electrical Engineering Program
Permanent link to this recordhttp://hdl.handle.net/10754/563748
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AbstractThis paper starts by introducing the Grünwald-Letnikov derivative, the Riesz potential and the problem of generalizing the Laplacian. Based on these ideas, the generalizations of the Laplacian for 1D and 2D cases are studied. It is presented as a fractional version of the Cauchy-Riemann conditions and, finally, it is discussed with the n-dimensional Laplacian.
CitationOrtigueira, M. D., Laleg-Kirati, T.-M., & Machado, J. A. T. (2014). Riesz potential versus fractional Laplacian. Journal of Statistical Mechanics: Theory and Experiment, 2014(9), P09032. doi:10.1088/1742-5468/2014/09/p09032
SponsorsThis work was partially funded by National Funds through the Foundation for Science and Technology of Portugal, under the project PEst-OE/EEI/UI0066/2011.