Problem 52120. Compute the fractional derivative

Cody Problem 1370 asks us to compute the derivative of a polynomial. This problem extends that idea to fractional derivatives, which appear in some models of mixing in rivers and other applications. Denote the qth derivative as D^q x^a. Then a familiar example from calculus would be D^2 x^3 = 6 x.
Fractional calculus involves derivatives in which the order q is not an integer. With q = 1/2 and a = 2, then
D^{1/2} x^2 = 8 x^{3/2} / (3 sqrt(pi))
Write a function that computes the fractional derivative of order q of an expression of the form
f(x) = c­1 x^a1 + c2 x^a2 + c3 x^a3 +...
The first input to the function will be a 2xn matrix in which the first row is the coefficients ci and the second row is the exponents ai. The output should be in a similar form.
Solve

Solution Stats

36.36% Correct | 63.64% Incorrect
Last Solution submitted on Jan 09, 2026

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