Fractional Differential Forms II

2003/01/13 by Kathleen Cotrill-Shepherd, Mark Naber, Cotrill-Shepherd, Kathleen +2
Mathematics · Physics and Astronomy · #Differential Equations and Numerical Methods #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical Physics (math-ph) #Nonlinear Differential Equations Analysis #math-ph #math.DG #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0301016

40 pages

arxiv created 2003/01/13 · openalex publication_date 2003/01/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This work further develops the properties of fractional differential forms. In particular, finite dimensional subspaces of fractional form spaces are considered. An inner product, Hodge dual, and covariant derivative are defined. Coordinate transformation rules for integral order forms are also computed. Matrix order fractional calculus is used to define matrix order forms. This is achieved by combining matrix order derivatives with exterior derivatives. Coordinate transformation rules and covariant derivative for matrix order forms are also produced. The Poincare' lemma is shown to be true for exterior fractional differintegrals of all orders excluding those whose orders are non-diagonalizable matrices.

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