The re-configurable filter allows independent tuning of frequency and changes the frequency response of the filter without switching the circuit components. Here, fractional-capacitors and fractional-inductors are used to design a re-configurable fractional order band-stop and all-pass filter to replicate the frequency domain behavior of each other. The proposed filter has been tested in the frequency range of 10 Hz to 10 MHz. The primary aim of this article is to realize, the design parameters (center frequency and bandwidth) of re-configurable filters using fractional order topology, where tunability of filter components is not reliable. To explore the dependence of notches and all-pass characteristics with the variation of fractional exponents of both the proposed filters, the simulation studies have been carried out by varying the exponents (α, β) from 0.1 to 1.0 with a step of 0.1 maintaining one exponent fixed and vice-versa. It is observed experimentally that a re-configurable integer order (IO) band-stop filter can be designed by using fractional value of order (i.e., α=0.5 and β=0.7) of all-pass filter. The stability of the proposed filters has also been investigated by observing the step response of the filter. Finally, the Python software was used to characterize the design parameters of the suggested filters and it was observed that the frequency response of the proposed filters shifts to their IO counterpart at those orders (i.e., α=0.5 and β=0.7). Hence, the flexibility in obtaining the notch frequency in fractional-order all-pass filter using the exponents α and β helps the researchers to realize a band-stop filter with desired specifications.