Riemann–Liouville integral
Okay, so have you ever played with building blocks and stacked them on top of each other? Well, imagine that instead of blocks, we have a bunch of shapes like triangles or circles that we want to stack on top of each other.
Now, let's say we want to find out how much area all of these shapes take up when we stack them together. That's kind of like what the Riemann-Liouville integral is. It's a way to measure the area under a curve, kind of like how we measure the area of a bunch of shapes stacked on top of each other.
But here's where it gets a little more complicated. Not all curves are straight lines, right? Sometimes they're curved or wavy or have lots of little bumps. So how do we measure the area under those types of curves?
That's where the Riemann-Liouville integral comes in. Instead of just measuring areas with straight lines, it lets us measure areas under curves that are curved or wavy or bumpy.
Basically, what happens is we divide up the curve we want to measure into tiny little pieces (kind of like cutting up a pizza into slices). Then we add up the areas of all these tiny little pieces to get an estimate of the total area under the curve.
It's not a perfect method, since we're just estimating, but it's a really useful way to measure areas under all sorts of different types of curves.
Now, let's say we want to find out how much area all of these shapes take up when we stack them together. That's kind of like what the Riemann-Liouville integral is. It's a way to measure the area under a curve, kind of like how we measure the area of a bunch of shapes stacked on top of each other.
But here's where it gets a little more complicated. Not all curves are straight lines, right? Sometimes they're curved or wavy or have lots of little bumps. So how do we measure the area under those types of curves?
That's where the Riemann-Liouville integral comes in. Instead of just measuring areas with straight lines, it lets us measure areas under curves that are curved or wavy or bumpy.
Basically, what happens is we divide up the curve we want to measure into tiny little pieces (kind of like cutting up a pizza into slices). Then we add up the areas of all these tiny little pieces to get an estimate of the total area under the curve.
It's not a perfect method, since we're just estimating, but it's a really useful way to measure areas under all sorts of different types of curves.