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Local Fractional Inequalities

  • George A. AnastassiouEmail author
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Abstract

This research is about inequalities in a local fractional setting. The author presents the following types of analytic local fractional inequalities: Opial, Hilbert-Pachpatte, Ostrowski, comparison of means, Poincare, Sobolev, Landau, and Polya–Ostrowski. The results are with respect to uniform and Lp norms, involving left and right Riemann–Liouville fractional derivatives. We derive also several interesting special cases.

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References

  1. 1.
    F.B. Adda, J. Cresson, Fractional differentiation equations and the Schrödinger equation. Appl. Math. Comput. 161, 323–345 (2005)MathSciNetzbMATHGoogle Scholar
  2. 2.
    G.A. Anastassiou, Quantitative Approximations (CRC Press, Boca Raton, 2001)zbMATHGoogle Scholar
  3. 3.
    G.A. Anastassiou, Fractional Differentiation Inequalities (Springer, Heidelberg, 2009)CrossRefGoogle Scholar
  4. 4.
    G.A. Anastassiou, Probabilistic Inequalities (World Scientific, Singapore, 2010)zbMATHGoogle Scholar
  5. 5.
    G.A. Anastassiou, Advanced Inequalities (World Scientific, Singapore, 2010)CrossRefGoogle Scholar
  6. 6.
    G.A. Anastassiou, Intelligent Mathematics: Computational Analysis (Springer, Heidelberg, 2011)CrossRefGoogle Scholar
  7. 7.
    G.A. Anastassiou, Advances on Fractional Inequalities (Springer, Heidelberg, 2011)CrossRefGoogle Scholar
  8. 8.
    G.A. Anastassiou, Intelligent Comparisons: Analytic Inequalities (Springer, Heidelberg, 2016)CrossRefGoogle Scholar
  9. 9.
    G.A. Anastassiou, Local fractional Taylor formula. J. Comput. Anal. Appl. 28, 709–713 (2020)Google Scholar
  10. 10.
    K. Diethelm, The Analysis of Fractional Differential Equations (Springer, Heidelberg, 2010)CrossRefGoogle Scholar
  11. 11.
    K.M. Kolwankar, Local fractional calculus: a review. arXiv: 1307:0739v1 [nlin.CD] (2013)Google Scholar
  12. 12.
    K.M. Kolwankar, A.D. Gangal, Local Fractional Calculus: A Calculus for Fractal Space-Time. Fractals: Theory and Applications in Engineering (Springer, New York, 1999), pp. 171–181Google Scholar
  13. 13.
    Z. Opial, Sur une inégalité. Ann. Polon. Math. 8, 29–32 (1960)MathSciNetCrossRefGoogle Scholar
  14. 14.
    A. Ostrowski, Über die Absolutabweichung einer differentiebaren Funktion von ihrem Integralmittelwert. Comment. Math. Helv. 10, 226–227 (1938)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of MemphisMemphisUSA

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