The two-dimensional fractional orthogonal derivative

2020/12/28 by Enno Diekema, Diekema, Enno
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fractional Differential Equations Solutions #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #math.CA

paper · pdf · doi:10.48550/arxiv.2012.14189

arxiv created 2020/12/28 · openalex publication_date 2020/12/28 · arxiv updated 2020/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is an edited and shortened version of Chapter 6 from the thesis of the author. First the one dimensional orthogonal derivative will be extended to the two-dimensional case. In the two-dimensional case we have to define the region of integration. In this paper we treat the integration over the square region and over the triangle region where in the last case we use biorthogonal polynomials expressed in terms of Appell functions. Next the two-dimensional orthogonal derivative will be extended to the two-dimensional fractional orthogonal derivative. The results are highly dependent on the F₁, F₂ and F₃ Appell functions.

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