On Applications of Fractional Derivatives in Electromagnetic Theory

In this paper, concepts of fractional-order (FO) derivatives are analysed from the point of view of applications in the electromagnetic theory. The mathematical problems related to the FO generalization of Maxwell's equations are investigated. The most popular formulations of the fractional derivatives, i.e., Riemann-Liouville, Caputo, Grünwald-Letnikov and Marchaud definitions, are considered. Properties of these derivatives are evaluated. It is demonstrated that some of formulations of the FO derivatives have limited applicability in the electromagnetic theory. That is, the Riemann-Liouville and Caputo derivatives with finite base point have a limited applicability whereas the Grünwald-Letnikov and Marchaud derivatives lead to reasonable generalizations of Maxwell's equations.