N. Engheta, A NOTE ON FRACTIONAL CALCULUS AND THE IMAGE METHOD FOR DIELECTRIC SPHERES, Journal of electromagnetic waves and applications, 9(9), 1995, pp. 1179-1188
In this note, we present an alternative mathematical way of expressing
electrostatic image charges for dielectric spheres using the concept
of fractional calculus. It is shown that the distributions of image ch
arges for the dielectric sphere (Lindell's solution) and the image cha
rges for the perfectly conducting ungrounded spheres (Lord Kelvin's so
lution) can be mathematically related via fractional differintegration
, and that the order of such fractional operators depend of the dielec
tric property of the sphere, i.e., its dielectric constant.