The Caputo fractional α-derivative, 0<α<1, for non-smooth functions with 1+α regularity is calculated by numerical computation. Let I be an interval and Dα(I) the set of all f(x) which satisfy f(x)=f(c)+f′(c)(x−a)+gc(x)(x−c)|(x−c)|α, where x,c∈I gc(x) a continuous function each c. We first extend trapezoidal method on rewrite integrand integral as product two differentiable functions. In ...