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Basic Abstract Fractional Monotone Approximation

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Abstract Fractional Monotone Approximation, Theory and Applications

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 411))

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Abstract

Here we extend our earlier fractional monotone approximation theory to abstract fractional monotone approximation, with applications to Prabhakar fractional calculus and non-singular kernel fractional calculi.

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References

  1. Anastassiou, G.A.: Bivariate Monotone Approximation. Proc. Amer. Math. Soc. 112(4), 959–964 (1991)

    Article  MathSciNet  Google Scholar 

  2. Anastassiou, G.A.: Frontiers in Approximation Theory. World Scientific Publishing Co Pte Ltd., New Jersey, Singapore (2015)

    Book  Google Scholar 

  3. Anastassiou, G.A.: Foundations of Generalized Prabhakar-Hilfer fractional Calculus with Applications. Cubo (2021, accepted)

    Google Scholar 

  4. Anastassiou, G.A.: Multiparameter fractional differentiation with non singular kernel. Issues Anal (2021, accepted)

    Google Scholar 

  5. Anastassiou, G.A.: Abstract fractional monotone approximation with applications (2021, submitted)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  7. Atangana, A., Baleanu, D.: New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model. Therm. Sci. 20(2), 763–769 (2016)

    Article  Google Scholar 

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

    Google Scholar 

  9. Giusti, A., et al.: A practical guide to Prabhakar fractional calculus. Fractional Calc. Appl. Anal. 23(1), 9–54 (2020)

    Article  MathSciNet  Google Scholar 

  10. Gorenflo, R., Kilbas, A., Mainardi, F., Rogosin, S.: Mittag-Leffler Functions. Related Topics and Applications. Springer, Heidelberg, New York (2014)

    MATH  Google Scholar 

  11. Hewitt, E., Stromberg, K.: Real and Abstract Analysis. Springer, New York, Heidelberg, Berlin (1965)

    Google Scholar 

  12. Losada, J., Nieto, J.J.: Properties of a new fractional derivative without singular kernel. Progr. Fract. Differ. Appl. 1(2), 87–92 (2015)

    Google Scholar 

  13. Polito, F., Tomovski, Z.: Some properties of Prabhakar-type fractional calculus operators. Fractional Differ. Calc. 6(1), 73–94 (2016)

    Article  MathSciNet  Google Scholar 

  14. Saxena, R.K., Kalla, S.L., Saxena, R.: Integr. Transf. Spec. Funct. Multivariate analogue of generalized Mittag-Leffler function 22(7), 533–548 (2011)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  16. Srivastava, H.M., Daoust, M.C.: A note on the convergence of Kompe’ de Feriet’s double hypergeometric series. Math. Nachr. 53, 151–159 (1972)

    Article  MathSciNet  Google Scholar 

  17. Teljakovskii, S.A.: Two theorems on the approximation of functions by algebraic polynomials. Mat. Sb. 70(112), 252–265 (1966) [Russian]; Amer. Math. Soc. Trans. 77(2), 163–178 (1968)

    Google Scholar 

  18. Trigub, R.M.: Approximation of functions by polynomials with integer coefficients. Izv. Akad. Nauk SSSR Ser. Mat. 26, 261–280 (1962) [Russian]

    Google Scholar 

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Anastassiou, G.A. (2022). Basic Abstract Fractional Monotone Approximation. In: Abstract Fractional Monotone Approximation, Theory and Applications. Studies in Systems, Decision and Control, vol 411. Springer, Cham. https://doi.org/10.1007/978-3-030-95943-2_1

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  • DOI: https://doi.org/10.1007/978-3-030-95943-2_1

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