Abstract fractional monotone approximation with applications


Here we extended our earlier fractional monotone approximation theory to abstract fractional monotone approximation, with applications to Prabhakar fractional calculus and non-singular kernel fractional calculi. We cover both the left and right sides of this constrained approximation. Let f ∈ Cp ([−1, 1]), p ≥ 0 and let L be a linear abstract left or right fractional differential operator such that L( f ) ≥ 0 over [0, 1] or [−1, 0], respectively. We can find a sequence of polynomials Qn of degree ≤ n such that L(Qn ) ≥ 0 over [0, 1] or [−1, 0], respectively. Additionally f is approximated quantitatively with rates uniformly by Qn with the use of first modulus of continuity of f(p) .

Publication Title

Fractal and Fractional