Fractional derivative
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10-28-2022, 11:35 AM
Post: #1
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Fractional derivative
hello, I propose a program that calculates the fractional derivatives. Comments and corrections to the program are appreciated. Thank you very much, robmio:
DerFraz((variable)->f(variable),n,a) --> --> where "n" is the degree of derivation, while "a" is the lower limit of the integral of the "fractional derivative of Riemann-Liouville" (see https://www.youtube.com/watch?v=2dwQUUDt...orphocular). Wolfram Mathematica 13.1 adopts "a=0". for example, the semiderivative of x^2 corresponds to: DerFraz((x)->x^2,1/2,0) --> (8*x*sqrt(x))/(3*pi) and here is the reverse process: DerFraz((x)->(8*x*sqrt(x))/(3*pi),-1/2,0) --> x^2. Code:
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10-29-2022, 03:40 PM
Post: #2
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RE: Fractional derivative
here is the modified program:
Code:
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10-29-2022, 04:17 PM
Post: #3
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RE: Fractional derivative
Quote:fnz:=(x)->fnz(purge(x)); What does fnz(x) do? Recursion without a base case ... does it cause infinite recursions? Also, why purge(x)? It seems x is function argument, thus already local variable. |
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10-29-2022, 07:05 PM
Post: #4
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RE: Fractional derivative
(10-29-2022 04:17 PM)Albert Chan Wrote:Quote:fnz:=(x)->fnz(purge(x)); with this instruction I tried not to make the "x" variable appear in the HP Prime CasVar. In this way, however, I cannot calculate some derivatives such as "DerFraz((x)->exp(x), 23 / 100,0). Can you help me? |
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10-31-2022, 12:21 PM
Post: #5
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RE: Fractional derivative
(10-29-2022 04:17 PM)Albert Chan Wrote:Quote:fnz:=(x)->fnz(purge(x)); In the end I prefer to use the "assume()" statement outside the program. Whenever I want to calculate the fractional derivative, on the "cas" screen I write: assume (t>0 and t>x), and the program works fine. Code:
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