Here is introduced a right general fractional derivative Caputo style with respect to a base absolutely continuous strictly increasing function g. We give various examples of such right fractional derivatives for different g. Let f be p-times continuously dif- ferentiable function on [a, b], and let L be a linear right general fractional differential operator such that L(f) is non-negative over a critical closed subinterval J of [a,b]. We can find a sequence of polynomials Qn of degree less-equal n such that L(Qn) is non-negative over J, furthermore f is approximated uniformly by Qn over [a, b] . The degree of this constrained approximation is given by an inequality using the first modulus of continuity of f(p). We finish we applications of the main right fractional monotone approximation theorem for different g.