Fractional vector calculus and fractional Maxwell's equations
- Skobeltsyn Institute of Nuclear Physics, Moscow State University, Leninskie gory, Moscow 119991 (Russian Federation), E-mail: tarasov@theory.sinp.msu.ru
The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. 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. We solve some problems of consistent formulations of FVC by using a fractional generalization of the Fundamental Theorem of Calculus. We define the differential and integral vector operations. The fractional Green's, Stokes' and Gauss's theorems are formulated. The proofs of these theorems are realized for simplest regions. A fractional generalization of exterior differential calculus of differential forms is discussed. Fractional nonlocal Maxwell's equations and the corresponding fractional wave equations are considered.
- OSTI ID:
- 21163677
- Journal Information:
- Annals of Physics (New York), Vol. 323, Issue 11; Other Information: DOI: 10.1016/j.aop.2008.04.005; PII: S0003-4916(08)00059-6; Copyright (c) 2008 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
- Country of Publication:
- United States
- Language:
- English
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