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
All original content copyright, © 2011-2024. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
