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Frequency and Time Domain Solution for Dynamic Systems having Differential Equations of Continuous Order

Shantanu Das


Fractional Differential Equations, when generalized to have a continuous order, the dynamic system has interesting transfer functions and interesting and advantageous properties. The method is discussed to have these system responses defined in frequency and time domain. Interestingly a pure continuous order system has no poles in the left half of frequency domain, the time solution is thus obtained via Laplace inverse, by integration on the branch cut in form of Bestimmte integral. In this paper continuous order low pass filter and high pass filter frequency and time responses as Green’s function is obtained for system of differential equation with continuous order.


Bestimmte Integral, discrete order, continuous order, fractional differential equation, residue of poles, integration on branch-cut, several memory relaxations.

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