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The left Riemann-Liouville fractional derivative is defined as (2.1).
The left Riemann-Liouville fractional integral and the right Riemann-Liouville fractional integral are defined respectively by (1).
Thus the area chosen to represent a single slice in a Riemann sum will be either its width or 0 depending upon whether we pick a rational x or not at which to evaluate our integrand in that interval.
In order to find this, a Riemann sum was executed.
Figure 3 is an illustration to help visualize how the Riemann sum works.
By taking a Riemann sum of these sample points, the area under the AC signal would be obtained and the change in potential could be found.
In order to find the angle swept by the eye from a voltage reading by the circuitry, a Riemann sum was utilized.
To illustrate the operation of our state machines' integration, a visual depiction of the Riemann sum over an amplified eye signal depicted on an oscilloscope.
For this function no matter how small the intervals are, you can have a Riemann sum of 0 or of b - a.
A Riemann sum is basically a numerical approximation of an integral that finds the area under a curve by breaking it up into small rectangles and adding up all the individual areas.
In the riemannSum state, the program performed a running Riemann sum with ADC values as rectangle heights and a constant for rectangle width, since our refresh rate was constant.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com