Swiss Micros DM32: Reimann-Louiville Fractional Integral of x^p
Introduction
The program presented today calculates the Riemann-Louiville integral of:
f(t) = t^p, where p is a real number.
The formula for this integral is:
cDx^(-v) = 1 / Γ(v) * ∫( (x – t) * t^p dt, t = c, t = x)
= ∫( ((x – t) * t^p) / (v -1)! dt, t = c, t = x)
I covered these type of integrals on my September 14, 2024 blog.
DM32 Program: Reimann-Louiville Fractional Integral of x^p
LBL F
INPUT C
INPUT X
INPUT V
INPUT P
FN= I
RCL C
RCL X
∫ FN d T
RTN
LBL I
RCL X
RCL- T
RCL V
1
-
y^x
RCL T
RCL P
y^x
×
RCL V
1
-
x!
÷
RTN
Here is a text version that can be transferred to a dm32 state file (fractionalintegralm.d32):
https://drive.google.com/file/d/1E-wUq4GW5dX06VZ-5WWwy7KRm3SN_uyq/view?usp=sharing
Examples
Run program F: XEQ F. Make sure that V > 0.
C |
X |
V |
P |
Result (FIX 5) |
0 |
5 |
2 |
2 |
52.08333 |
1 |
6 |
3 |
3 |
385.41667 |
2 |
7 |
1.5 |
3 |
717.69103 |
0 |
1 |
1.75 |
4 |
0.05298 |
Source
Kimeu, Joseph M., "Fractional Calculus: Definitions and Applications" (2009).Masters Theses & Specialist Projects. Paper 115. http://digitalcommons.wku.edu/theses/115
Eddie
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