Right general fractional monotone approximation

Abstract

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(Q_n) is non-negative over J, furthermore f is approximated uniformly by Q_n 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.