Journal ArticleDOI
Applications of fractional exterior differential in three-dimensional space
TLDR
In this paper, a brief survey of fractional calculus and fractional differential forms was given, and the fractional exterior transition to curvilinear coordinate at the origin was discussed.Abstract:
A brief survey of fractional calculus and fractional differential forms was firstly given The fractional exterior transition to curvilinear coordinate at the origin were discussed and the two coordinate transformations for the fractional differentials for three-dimensional Cartesian coordinates to spherical and cylindrical coordinates are obtained, respectively In particular, for v=m=1, the usual exterior transformations, between the spherical coordinate and Cartesian coordinate, as well as the cylindrical coordinate and Cartesian coordinate, are found respectively, from fractional exterior transformationread more
Citations
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Journal ArticleDOI
Fractional vector calculus and fractional Maxwell’s equations
TL;DR: The history of fractional vector calculus (FVC) has only 10 years as mentioned in this paper and the main approaches to formulate a FVC, which are used in the physics during the past few years, will be briefly described in this paper.
Book ChapterDOI
An Introduction to Noncommutative Differential Geometry and its Physical Applications: Extensions of Space-Time
Journal ArticleDOI
Geometry of fractional spaces
TL;DR: In this article, the relation between fractional calculus and fractal geometry is clarified, showing that fractional spaces can be regarded as fractals when the ratio of their Hausdorff and spectral dimension is greater than one.
Book ChapterDOI
Fractional Vector Calculus
TL;DR: In this article, the fractional Green's, Stokes' and Gauss' theorems are formulated for simplest regions and a fractional generalization of exterior differential calculus of differential forms is discussed.
Journal ArticleDOI
Fractional integro-differential calculus and its control-theoretical applications. I. Mathematical fundamentals and the problem of interpretation
TL;DR: The review is devoted to using the fractional integro-differential calculus for description of the dynamics of various systems and control processes.
References
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Book
An Introduction to Noncommutative Differential Geometry and Its Physical Applications
TL;DR: In this article, the authors introduce differential geometry, non-commutative geometry, vector bundles, cyclic homology, and extensions of space-time, and show how these can be combined.
Book ChapterDOI
An Introduction to Noncommutative Differential Geometry and its Physical Applications: Extensions of Space-Time
Journal ArticleDOI
Fractional Differential Forms
TL;DR: In this article, a generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders, and the metric for the fractional form spaces is given, based on the coordinate transformation rules.
Journal ArticleDOI
Fractional differential forms
TL;DR: In this paper, a generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders, and the metric for the fractional form spaces is given, based on the coordinate transformation rules.
Journal ArticleDOI
Z_3-graded exterior differential calculus and gauge theories of higher order
TL;DR: In this paper, a generalization of the exterior differential calculus, based on the operator d such that d^3 = 0, but d^2
ot=0, is presented.