Peano Kernels of Fractional Delay Systems

In this paper, design and analysis of fractional delay systems in time-domain is proposed. Under the condition of exactness, we prove that the difference between the desired output signal and the actual output of the system can be represented as the convolution of the derivative of the input signal and the Peano kernel. The Peano kernel are solved analytically in this article. We also solve the weighting coefficients in closed form when the degree of exactness is equal to the number of coefficients.