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Fractional vector calculus and fractional Maxwell’s equations. (English) Zbl 1180.78003

The fractional calculus has a long history, dating from 30 September 1695 when a derivative of order \(1/2\) was described by Leibniz. However, the history of the fractional vector calculus (FVC) is short, as it dates back only 10 years. This paper describes some different approaches to the formulation of the FVC which have been used in physics dring the last 10 years. Various generalizations are given, including the fractional Green’s and Stokes’ theorems, and also the theorems due to Gauss.

MSC:

78A02 Foundations in optics and electromagnetic theory
78A25 Electromagnetic theory (general)
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