Analytical expression of time domain response of arbitrary order fractance

Fractance is the terminology for any integro-differential operator which its order can be fractional. It is often cited in various disciplines such as biomédical engineering, control engineering and electronic engineering etc., which are the crucial basis in the design and implementation of signal processing systems. Since analytically obtaining time domain response of fractance yields advantage in many circumstances, an analytical expression of such response has been derived in this research where the fractance under consideration can be of arbitrary order even though the magnitude of such order may be greater than unity. This expression has been found to be an efficient mathematical tool for those aforementioned fractance involved disciplines which support the signal processing system design and implementation.