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(77 citation statements)

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“…The fractional‐order nature of the integration operator, s −δ , makes it digitally nonimplementable. Hence, the fractional integral operator is approximated using a fifth‐order Oustaloup's recursive filter in order to practically implement it using an embedded computers . The lower and upper bounds of the translational frequencies of the filter are empirically selected as ω L = 10 −3 rad/s and ω H = 10 3 rad/s, respectively .…”

confidence: 99%

“…The fractional‐order nature of the integration operator, s −δ , makes it digitally nonimplementable. Hence, the fractional integral operator is approximated using a fifth‐order Oustaloup's recursive filter in order to practically implement it using an embedded computers . The lower and upper bounds of the translational frequencies of the filter are empirically selected as ω L = 10 −3 rad/s and ω H = 10 3 rad/s, respectively .…”

confidence: 99%

“…For continuous implementation, pole-zero pairs should be in the negative real axis of -plane and for discrete implementation, pole-zero pairs should lie within the unit circle of -plane. More number of pole-zero pairs exhibit better and close approximation, but increases the memory requirements and complexity; however, the advent of modern powerful software can easily deal with additional complexity [106].…”

confidence: 99%

“…The fractional operator is denoted by G γ ; where, γ is the positive and real numbered exponent of the operator. The three common definitions of fractional operation are provided by Riemann‐Liouville, Gruunwald‐Letnikov, and Caputo in Equations (25) to (27), respectively $${G}^{\gamma}f\left(t\right)=\frac{1}{\Gamma \left(n-\gamma \right)}\frac{{d}^{n}}{{\mathrm{italicdt}}^{n}}{\int}_{a}^{t}\frac{f\left(\tau \right)}{{\left(t-\tau \right)}^{\gamma -n+1}}\mathrm{italicd\tau},$$ …”

confidence: 99%