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Caputo and Canavati Fractional Approximation by Choquet Integrals |
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PP: 7-20 |
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doi:10.18576/pfda/050102
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Author(s) |
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George A. Anastassiou,
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Abstract |
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| Here we consider the quantitative Caputo and Canavati fractional approximation of positive sublinear operators to the unit
operator. At the beginning we perform the investigation of the fractional rate of the convergence of the Bernstein-Kantorovich-Choquet
and Bernstein-Durrweyer-Choquet polynomial Choquet-integral operators. After that we discuss the very general comonotonic positive
sublinear operators based on the representation theorem of Schmeidler (1986) [1]. We ended with the approximation by the very
general direct Choquet-integral form positive sublinear operators. All fractional approximations are presented via inequalities implying
the modulus of continuity of the approximated function fractional order derivative. |
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