Analysis and results of prey-predator population system indicate that the fractional model match the anomalous biological diffusion behavior observed in the field.
SBL fitting method provides straightforward solutions to obtain an integer order model approximation of fractional order operators and systems according to matching points from SBL of fractional order systems in desired frequency ranges.
The process of matching with requires a fractional decimation of, which is achieved by resampling at.
To compare the performances with other methods, H.264 (main profile, JM 15.1, Search range: 7 pixels, Type of block matching algorithm: UMHexagon Search, QP: 28, Adopted fractional-pixel accuracy: 1/4 pixel, Entropy coding method: CAVLC) and CPM/NCIM are used.
Also, the fractional derivative (D_t^{ralpha }) of (Res x,t)) and (Res_k x,t)) is matching at (t=0) for each (r=0,1,2,ldots,k).
Different approaches are explored in order to transform the integer order model into a reduced order fractional model able to match the dynamic response of the initial system.
Taking harmonic chain as an example, we add a power function of fractional order to Taylor expansion of the dispersion relation, and determine the parameters by matching two selected wave numbers.
In our studies we used custom built PZT ultrasound transducers (d = 35 mm) having a single quarter-wave matching layer, a center frequency of 0.53 MHz, and a −6 dB fractional bandwidth of 65% with two peaks (0.44 MHz, 0.66 MHz).
Fractional-pixel accuracy MCP [13], which is adopted in the latest video coding standards, performs block matching on interpolated reference frames.
Based on a new design theory for broadband impedance matching circuits, we designed a slot antenna with a small radiation resistance of 1 Ω impedance matched to a three-pole Chebyshev bandpass filter with 10 GHz center frequency and 0.35% fractional bandwidth.
