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The Linear Scale Invariant Systems are introduced for both integer and fractional orders. They are defined by the generalized Euler-Cauchy differential equation. It is shown how to compute the impulse responses corresponding to the two regions of convergence of the transfer function. This is obtained by using the Mellin transform. The quantum fractional derivatives are used because they are suitable for dealing with this kind of systems.

ON THE LINEAR SCALE FRACTIONAL SYSTEMS - An Application of the Fractional Quantum Derivative