Discretized fractional calculus
SIAM Journal on Mathematical Analysis
Digital filter design
Analysis and design of fractional-order digital control systems
Systems Analysis Modelling Simulation
A new IIR-type digital fractional order differentiator
Signal Processing - Special issue: Fractional signal processing and applications
Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering
Impulse invariance-based method for the computation of fractional integral of order 0
Computers and Electrical Engineering
On distributed order integrator/differentiator
Signal Processing
Stability of fractional-order linear time-invariant systems with multiple noncommensurate orders
Computers & Mathematics with Applications
Fractional models for modeling complex linear systems under poor frequency resolution measurements
Digital Signal Processing
Non-fragile observer design for fractional-order one-sided Lipschitz nonlinear systems
International Journal of Automation and Computing
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In this paper, we derive the impulse response of a fractional second order filter of the form (s^2+as+b)^-^@c, where a,b=0 and @c0. The asymptotic properties of the impulse responses are obtained. Moreover, based on the derived analytical impulse response, we show how to perform the discretization of the above fractional second order filter. Finally, a number of illustrated examples in time and frequency domains are provided as proofs of concepts.