2002/05/24 by W. Chen, Wen Chen, Chen, W.
Computer Science · Mathematics · #Computational Engineering #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Finance #Fractional Differential Equations Solutions #G1.8 #G1.9 #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #and Science (cs.CE) #cs.CE #cs.CG
paper · pdf · doi:10.48550/arxiv.cs/0205063
Welcome any comments to [email protected]
arxiv created 2002/05/24 · openalex publication_date 2002/05/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Report II is concerned with the extended results of distance function wavelets (DFW). The fractional DFW transforms are first addressed relating to the fractal geometry and fractional derivative, and then, the discrete Helmholtz-Fourier transform is briefly presented. The Green second identity may be an alternative devise in developing the theoretical framework of the DFW transform and series. The kernel solutions of the Winkler plate equation and the Burger's equation are used to create the DFW transforms and series. Most interestingly, it is found that the translation invariant monomial solutions of the high-order Laplace equations can be used to make very simple harmonic polynomial DFW series. In most cases of this study, solid mathematical analysis is missing and results are obtained intuitively in the conjecture status.