Electromagnetic Interpretation of Fractional-Order Elements

Abstract

Fractional circuits have attracted extensive attention of scholars and researchers for their superior performance and potential applications. Recently, the fundamentals of the conventional circuit theory were extended to include the new generalized elements and fractional-order elements. As is known to all, circuit theory is a limiting special case of electromagnetic field theory and the characterization of classical circuit elements can be given an elegant electromagnetic interpretation. In this paper, considering fractional-order time derivatives, an electromagnetic field interpretation of fractional-order elements: fractional-order inductor, fractional-order capacitor and fractional-order mutual inductor is presented, in terms of a quasi-static expansion of the fractional Maxwell's equations. It shows that fractional-order elements can also be interpreted as a fractional electromagnetic system. As the element order equals to 1, the interpretation of fractional-order elements matches that of the classical circuit elements: L, C, and mutual inductor, respectively.

Fractional Derivative Modification of Drude Model

“…Fractional calculus, the branch of mathematics devoted to studying non-integer-order derivatives and integrals, has become an increasingly popular tool for analysis of various problems in physics, ranging from quantum mechanics and cosmology [ 1 ] to electric circuits [ 2 ] and electromagnetic wave propagation [ 3 ]. An extensive review of recent developments is presented in [ 4 ].…”

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“…Factional calculus -branch of mathematics devoted to study non-integer order derivatives and integrals, becomes an increasingly popular tool for analysis of various problems in physics, ranging from quantum mechanics and cosmology [1] to electric circuits [2] and electromagnetic wave propagation [3]. An extensive review of recent developments is presented in [4].…”