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

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers8

Suggested Problems

More from this Author319

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!