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Cubo (Temuco)

versão On-line ISSN 0719-0646


ANASTASSIOU, George A. Right General Fractional Monotone Approximation. Cubo [online]. 2015, vol.17, n.3, pp.01-14. ISSN 0719-0646.

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 differentiable 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.

Palavras-chave : Right Fractional Monotone Approximation; general right fractional derivative; linear general right fractional differential operator; modulus of continuity.

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