Abstract
ABSTRACTThe Maxwell equations play a vital role in the electromagnetic theory. With the development of Fractional Calculus and its applications, new fractional Maxwell equations are required to describe fractional electromagnetic fields. In this paper, the fractional electromagnetic induction law is presented with considering the properties of fractional inductance. Based on this, we have obtained the fractional Maxwell equations. In addition, the non-homogeneous fractional wave equations and the homogeneous fractional vector Helmholtz equations are deduced. Using these results, we investigate the behavior of electromagnetic waves in fractional circular waveguides with fractional-order inductance characteristics. The results show that the electromagnetic fields change with different fractional orders.
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