Abstract:We examine the localized mode and the transmission of plane waves across a capacitive impurity of strength $\Delta$, in a 1D bi-inductive electrical transmission line where the usual discrete Laplacian is replaced by a fractional one characterized by a fractional exponent $s$. In the absence of the impurity, the plane wave dispersion is computed in closed form in terms of hypergeometric functions. It is observed that the bandwidth decreases steadily, as $s$ decreases towards zero, reaching a minimum width at $… Show more
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