Approximation of Laplace transform of fractional derivatives via Clenshaw–Curtis integration

In this paper, we approximate the Laplace transform of fractional derivatives via Clenshaw–Curtis integration. The idea of applying Chebyshev polynomial to the numerical computation of integrals is extended to Laplace transform of fractional derivatives. The numerical stability of forward recurrence relations is considered, which depends on the asymptotic behaviour of the coefficients. Error estimation for the Laplace approximation of the fractional derivatives is also considered. Finally, from the numerical examples, the method seems to be promising for approximation of the Laplace transform of fractional derivative.