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Left Generalized High Order Fractional Monotone Approximation

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Part of the book series: Studies in Computational Intelligence ((SCI,volume 624))

Abstract

Here are used the left general fractional derivatives Caputo style with respect to a base absolutely continuous strictly increasing function.

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References

  1. G.A. Anastassiou, Higher order monotone approximation with linear differential operators. Indian J. Pure Appl. Math. 24(4), 263–266 (1993)

    MathSciNet  MATH  Google Scholar 

  2. G.A. Anastassiou, Fractional Differentiation Inequalities (Springer, New York, 2009)

    Book  MATH  Google Scholar 

  3. G.A. Anastassiou, The reduction method in fractional calculus and fractional Ostrowski type inequalities. Indian J. Math. 56(3), 333–357 (2014)

    MathSciNet  MATH  Google Scholar 

  4. G.A. Anastassiou, Univariate left fractional polynomial high order monotone approximation. Bull. Korean Math. Soc. 52(2), 593–601 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  5. G. Anastassiou, Univariate Left General High Order Fractional Monotone Approximation (2015) (submitted)

    Google Scholar 

  6. G.A. Anastassiou, O. Shisha, Monotone approximation with linear differential operators. J. Approx. Theory 44, 391–393 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  7. R.A. DeVore, G.G. Lorentz, Constructive Approximation (Springer, New York, 1993)

    Book  MATH  Google Scholar 

  8. K. Diethelm, The Analysis of Fractional Differential Equations. Lecture Notes in Mathematics, vol. 2004, 1st edn. (Spinger, New York, 2010)

    Google Scholar 

  9. H.H. Gonska, E. Hinnemann, Pointwise estimated for approximation by algebraic polynomials. Acta Math. Hungar. 46, 243–254 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  10. R.-Q. Jia, Chapter 3. Absolutely Continuous Functions, https://www.ualberta.ca/~rjia/Math418/Notes/Chap.3.pdf

  11. A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, vol. 204 (Elsevier, New York, 2006)

    Google Scholar 

  12. H.L. Royden, Real Analysis, 2nd edn. (Macmillan Publishing Co., Inc., New York, 1968)

    Google Scholar 

  13. A.R. Schep, Differentiation of Monotone Functions, http://people.math.sc.edu/schep/diffmonotone.pdf

  14. O. Shisha, Monotone approximation. Pacific J. Math. 15, 667–671 (1965)

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to George A. Anastassiou .

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Anastassiou, G.A., Argyros, I.K. (2016). Left Generalized High Order Fractional Monotone Approximation. In: Intelligent Numerical Methods: Applications to Fractional Calculus. Studies in Computational Intelligence, vol 624. Springer, Cham. https://doi.org/10.1007/978-3-319-26721-0_22

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  • DOI: https://doi.org/10.1007/978-3-319-26721-0_22

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  • Print ISBN: 978-3-319-26720-3

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