Negative Domain Local Fractional Inequalities

  • George A. AnastassiouEmail author
Part of the Studies in Computational Intelligence book series (SCI, volume 886)


This research is about inequalities in a local fractional environment over a negative domain. The author presents the following types of analytic local fractional inequalities: Opial, Hilbert–Pachpatte, comparison of means, Poincare and Sobolev. The results are with respect to uniform and \(L_{p}\) norms, involving left and right Riemann–Liouville fractional derivatives. See also [10].


  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(4), 709–713 (2020)Google Scholar
  10. 10.
    G.A. Anastassiou, Negative domain local fractional inequalities. J. Comput. Anal. Appl. 28(5), 879–891 (2020)Google Scholar
  11. 11.
    K. Diethelm, The Analysis of Fractional Differential Equations (Springer, Heidelberg, 2010)CrossRefGoogle Scholar
  12. 12.
    K.M. Kolwankar, Local fractional calculus: a review. arXiv: 1307:0739v1 [nlin.CD] 2 Jul 2013
  13. 13.
    K.M. Kolwankar, A.D. Gangal, Local fractional calculus: a calculus for fractal space-time, Fractals: Theory and Applications in Engineering (Springer, London, 1999), pp. 171–181CrossRefGoogle Scholar
  14. 14.
    Z. Opial, Sur une inégalité. Ann. Polon. Math. 8, 29–32 (1960)MathSciNetCrossRefGoogle Scholar
  15. 15.
    A. Ostrowski, Über die Absolutabweichung einer differentiebaren Funktion von ihrem Integralmittelwert. Comment. Math. Helv. 10, 226–227 (1938)CrossRefGoogle Scholar

Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of MemphisMemphisUSA

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