The transient behavior in the fractal admittance acting as a non-integer-rank differential/integral operator, Y(s) ∝ sa with -1a1 and a0, is examined from the point of view of memory effects by employing the distributed-relaxation-time model. The internal state of the diode is found to be represented by the current spectrum i(λ, t) with respect to the carrier relaxation rate λ, leading to a general formulation of the long-time-tail memory behavior characteristic of the operator. One-to-one corrsepondence is found among the input voltage in the past ν(-t), the short-circuit current isc(t) and the initial current spectrum i(λ, 0) within the framework of the Laplace-type integral transformation and its inverse, assuring that each response retains in principle the entire information on the corresponding input, such as the functional form, the magnitude, the onset time, and so forth. The current and voltage responses are exemplified for various single-pulse voltage inputs. The responses to the pulse-train inputs corresponding to different ASCII codes are found to be properly discriminated between one another, showing the potentials of the present memory effects.